Node List

Full API documentation: nodes

class mdp.nodes.PCANode

Filter the input data through the most significatives of its principal components.

Variables:
  • avg – Mean of the input data (available after training).
  • v – Transposed of the projection matrix (available after training).
  • d – Variance corresponding to the PCA components (eigenvalues of the covariance matrix).
  • explained_variance – When output_dim has been specified as a fraction of the total variance, this is the fraction of the total variance that is actually explained.

Reference

More information about Principal Component Analysis, a.k.a. discrete Karhunen-Loeve transform can be found among others in I.T. Jolliffe, Principal Component Analysis, Springer-Verlag (1986).

Full API documentation: PCANode

class mdp.nodes.WhiteningNode

Whiten the input data by filtering it through the most significant of its principal components.

All output signals have zero mean, unit variance and are decorrelated.

Variables:
  • avg – Mean of the input data (available after training).
  • v – Transpose of the projection matrix (available after training).
  • d – Variance corresponding to the PCA components (eigenvalues of the covariance matrix).
  • explained_variance – When output_dim has been specified as a fraction of the total variance, this is the fraction of the total variance that is actually explained.

Full API documentation: WhiteningNode

class mdp.nodes.NIPALSNode

Perform Principal Component Analysis using the NIPALS algorithm.

This algorithm is particularly useful if you have more variables than observations, or in general when the number of variables is huge and calculating a full covariance matrix may be infeasible. It’s also more efficient of the standard PCANode if you expect the number of significant principal components to be a small. In this case setting output_dim to be a certain fraction of the total variance, say 90%, may be of some help.

Variables:
  • avg – Mean of the input data (available after training).
  • d – Variance corresponding to the PCA components.
  • v – Transposed of the projection matrix (available after training).
  • explained_variance – When output_dim has been specified as a fraction of the total variance, this is the fraction of the total variance that is actually explained.

Reference

Reference for NIPALS (Nonlinear Iterative Partial Least Squares): Wold, H. Nonlinear estimation by iterative least squares procedures. in David, F. (Editor), Research Papers in Statistics, Wiley, New York, pp 411-444 (1966).

More information about Principal Component Analysis*, a.k.a. discrete Karhunen-Loeve transform can be found among others in I.T. Jolliffe, Principal Component Analysis, Springer-Verlag (1986).

Original code contributed by: Michael Schmuker, Susanne Lezius, and Farzad Farkhooi (2008).

Full API documentation: NIPALSNode

class mdp.nodes.FastICANode

Perform Independent Component Analysis using the FastICA algorithm.

Note that FastICA is a batch-algorithm. This means that it needs all input data before it can start and compute the ICs. The algorithm is here given as a Node for convenience, but it actually accumulates all inputs it receives. Remember that to avoid running out of memory when you have many components and many time samples.

FastICA does not support the telescope mode (the convergence criterium is not robust in telescope mode). criterium is not robust in telescope mode).

History:

  • 1.4.1998 created for Matlab by Jarmo Hurri, Hugo Gavert, Jaakko Sarela, and Aapo Hyvarinen
  • 7.3.2003 modified for Python by Thomas Wendler
  • 3.6.2004 rewritten and adapted for scipy and MDP by MDP’s authors
  • 25.5.2005 now independent from scipy. Requires Numeric or numarray
  • 26.6.2006 converted to numpy
  • 14.9.2007 updated to Matlab version 2.5
Variables:
  • white – The whitening node used for preprocessing.
  • filters – The ICA filters matrix (this is the transposed of the projection matrix after whitening).
  • convergence – The value of the convergence threshold.

Reference

Aapo Hyvarinen (1999). Fast and Robust Fixed-Point Algorithms for Independent Component Analysis IEEE Transactions on Neural Networks, 10(3):626-634.

Full API documentation: FastICANode

class mdp.nodes.CuBICANode

Perform Independent Component Analysis using the CuBICA algorithm.

Note that CuBICA is a batch-algorithm, which means that it needs all input data before it can start and compute the ICs. The algorithm is here given as a Node for convenience, but it actually accumulates all inputs it receives. Remember that to avoid running out of memory when you have many components and many time samples.

As an alternative to this batch mode you might consider the telescope mode (see the docs of the __init__ method).

Variables:
  • white – The whitening node used for preprocessing.
  • filters – The ICA filters matrix (this is the transposed of the projection matrix after whitening).
  • convergence – The value of the convergence threshold.

Reference

Blaschke, T. and Wiskott, L. (2003). CuBICA: Independent Component Analysis by Simultaneous Third- and Fourth-Order Cumulant Diagonalization. IEEE Transactions on Signal Processing, 52(5), pp. 1250-1256.

Full API documentation: CuBICANode

class mdp.nodes.TDSEPNode

Perform Independent Component Analysis using the TDSEP algorithm.

Note

That TDSEP, as implemented in this Node, is an online algorithm, i.e. it is suited to be trained on huge data sets, provided that the training is done sending small chunks of data for each time.

Variables:
  • white – The whitening node used for preprocessing.
  • filters – The ICA filters matrix (this is the transposed of the projection matrix after whitening).
  • convergence – The value of the convergence threshold.

Reference

Ziehe, Andreas and Muller, Klaus-Robert (1998). TDSEP an efficient algorithm for blind separation using time structure. in Niklasson, L, Boden, M, and Ziemke, T (Editors), Proc. 8th Int. Conf. Artificial Neural Networks (ICANN 1998).

Full API documentation: TDSEPNode

class mdp.nodes.JADENode

Perform Independent Component Analysis using the JADE algorithm.

Note that JADE is a batch-algorithm. This means that it needs all input data before it can start and compute the ICs. The algorithm is here given as a Node for convenience, but it actually accumulates all inputs it receives. Remember that to avoid running out of memory when you have many components and many time samples.

JADE does not support the telescope mode.


Reference

Cardoso, Jean-Francois and Souloumiac, Antoine (1993). Blind beamforming for non Gaussian signals. Radar and Signal Processing, IEE Proceedings F, 140(6): 362-370.

Cardoso, Jean-Francois (1999). High-order contrasts for independent component analysis. Neural Computation, 11(1): 157-192.

Original code contributed by: Gabriel Beckers (2008).


History

  • May 2005 version 1.8 for MATLAB released by Jean-Francois Cardoso
  • Dec 2007 MATLAB version 1.8 ported to Python/NumPy by Gabriel Beckers
  • Feb 15 2008 Python/NumPy version adapted for MDP by Gabriel Beckers

Full API documentation: JADENode

class mdp.nodes.SFANode

Extract the slowly varying components from the input data.

Variables:
  • avg – Mean of the input data (available after training)
  • sf – Matrix of the SFA filters (available after training)
  • d – Delta values corresponding to the SFA components (generalized eigenvalues). [See the docs of the get_eta_values method for more information]

Reference

More information about Slow Feature Analysis can be found in Wiskott, L. and Sejnowski, T.J., Slow Feature Analysis: Unsupervised Learning of Invariances, Neural Computation, 14(4):715-770 (2002).

Full API documentation: SFANode

class mdp.nodes.SFA2Node

Get an input signal, expand it in the space of inhomogeneous polynomials of degree 2 and extract its slowly varying components.

The get_quadratic_form method returns the input-output

function of one of the learned unit as a QuadraticForm object. See the documentation of mdp.utils.QuadraticForm for additional information.

Reference:

More information about Slow Feature Analysis can be found in Wiskott, L. and Sejnowski, T.J., Slow Feature Analysis: Unsupervised Learning of Invariances, Neural Computation, 14(4):715-770 (2002).

Full API documentation: SFA2Node

class mdp.nodes.VartimeSFANode

Extract the slowly varying components from the input data. This node can be understood as a generalization of the SFANode that allows non-constant time increments between samples.

In particular, this node numerically computes the integrals involved in the SFA problem formulation by applying the trapezoid rule.

Variables:
  • avg – Mean of the input data (available after training)
  • sf – Matrix of the SFA filters (available after training)
  • d – Delta values corresponding to the SFA components (generalized eigenvalues). [See the docs of the get_eta_values method for more information]

Reference

More information about Slow Feature Analysis can be found in Wiskott, L. and Sejnowski, T.J., Slow Feature Analysis: Unsupervised Learning of Invariances, Neural Computation, 14(4):715-770 (2002).

Full API documentation: VartimeSFANode

class mdp.nodes.ISFANode

Perform Independent Slow Feature Analysis on the input data.

Variables:
  • RP – The global rotation-permutation matrix. This is the filter applied on input_data to get output_data
  • RPC – The complete global rotation-permutation matrix. This is a matrix of dimension input_dim x input_dim (the ‘outer space’ is retained)
  • covs – A mdp.utils.MultipleCovarianceMatrices instance input_data. After convergence the uppermost output_dim x output_dim submatrices should be almost diagonal. self.covs[n-1] is the covariance matrix relative to the n-th time-lag

Note

They are not cleared after convergence. If you need to free some memory, you can safely delete them with:

>>> del self.covs
Variables:
  • initial_contrast – A dictionary with the starting contrast and the SFA and ICA parts of it.
  • final_contrast – Like the above but after convergence.

Note

If you intend to use this node for large datasets please have a look at the stop_training method documentation for speeding things up.

Reference

Blaschke, T. , Zito, T., and Wiskott, L. (2007). Independent Slow Feature Analysis and Nonlinear Blind Source Separation. Neural Computation 19(4):994-1021 (2007) http://itb.biologie.hu-berlin.de/~wiskott/Publications/BlasZitoWisk2007-ISFA-NeurComp.pdf

Full API documentation: ISFANode

class mdp.nodes.XSFANode

Perform Non-linear Blind Source Separation using Slow Feature Analysis. This node is designed to iteratively extract statistically independent sources from (in principle) arbitrary invertible nonlinear mixtures. The method relies on temporal correlations in the sources and consists of a combination of nonlinear SFA and a projection algorithm. More details can be found in the reference given below (once it’s published).

The node has multiple training phases. The number of training phases depends on the number of sources that must be extracted. The recommended way of training this node is through a container flow:

>>> flow = mdp.Flow([XSFANode()])
>>> flow.train(x)

doing so will automatically train all training phases. The argument x to the Flow.train method can be an array or a list of iterables (see the section about Iterators in the MDP tutorial for more info). If the number of training samples is large, you may run into memory problems: use data iterators and chunk training to reduce memory usage.

If you need to debug training and/or execution of this node, the suggested approach is to use the capabilities of BiMDP. For example:

>>> flow = mdp.Flow([XSFANode()])
>>> tr_filename = bimdp.show_training(flow=flow, data_iterators=x)
>>> ex_filename, out = bimdp.show_execution(flow, x=x)

this will run training and execution with bimdp inspection. Snapshots of the internal flow state for each training phase and execution step will be opened in a web brower and presented as a slideshow.


Reference

Sprekeler, H., Zito, T., and Wiskott, L. (2009). An Extension of Slow Feature Analysis for Nonlinear Blind Source Separation. Journal of Machine Learning Research. http://cogprints.org/7056/1/SprekelerZitoWiskott-Cogprints-2010.pdf

Full API documentation: XSFANode

class mdp.nodes.GSFANode

This node implements “Graph-Based SFA (GSFA)”, which is the main component of hierarchical GSFA (HGSFA).

For further information, see: Escalante-B A.-N., Wiskott L, “How to solve classification and regression problems on high-dimensional data with a supervised extension of Slow Feature Analysis”. Journal of Machine Learning Research 14:3683-3719, 2013

Full API documentation: GSFANode

class mdp.nodes.iGSFANode

This node implements “information-preserving graph-based SFA (iGSFA)”, which is the main component of hierarchical iGSFA (HiGSFA).

For further information, see: Escalante-B., A.-N. and Wiskott, L., “Improved graph-based {SFA}: Information preservation complements the slowness principle”, e-print arXiv:1601.03945, http://arxiv.org/abs/1601.03945, 2017.

Full API documentation: iGSFANode

class mdp.nodes.FDANode

Perform a (generalized) Fisher Discriminant Analysis of its input. It is a supervised node that implements FDA using a generalized eigenvalue approach.

Note

FDANode has two training phases and is supervised so make sure to pay attention to the following points when you train it:

  • call the train method with two arguments: the input data and the labels (see the doc string of the train method for details).
  • if you are training the node by hand, call the train method twice.
  • if you are training the node using a flow (recommended), the only argument to Flow.train must be a list of (data_point, label) tuples or an iterator returning lists of such tuples, not a generator. The Flow.train function can be called just once as usual, since it takes care of rewinding the iterator to perform the second training step.
Variables:
  • avg – Mean of the input data (available after training).
  • v – Transposed of the projection matrix, so that output = dot(input-self.avg, self.v) (available after training).

Reference

More information on Fisher Discriminant Analysis can be found for example in C. Bishop, Neural Networks for Pattern Recognition, Oxford Press, pp. 105-112.

Full API documentation: FDANode

class mdp.nodes.FANode

Perform Factor Analysis.

The current implementation should be most efficient for long data sets: the sufficient statistics are collected in the training phase, and all EM-cycles are performed at its end.

The execute method returns the Maximum A Posteriori estimate of the latent variables. The generate_input method generates observations from the prior distribution.

Variables:
  • mu – Mean of the input data (available after training).
  • A – Generating weights (available after training).
  • E_y_mtx – Weights for Maximum A Posteriori inference.
  • sigma – Vector of estimated variance of the noise for all input components.

Reference

More information about Factor Analysis can be found in Max Welling’s classnotes: http://www.ics.uci.edu/~welling/classnotes/classnotes.html , in the chapter ‘Linear Models’.

Full API documentation: FANode

class mdp.nodes.RBMNode

Restricted Boltzmann Machine node. An RBM is an undirected probabilistic network with binary variables. The graph is bipartite into observed (visible) and hidden (latent) variables. By default, the execute method returns the probability of one of the hiden variables being equal to 1 given the input. Use the sample_v method to sample from the observed variables given a setting of the hidden variables, and sample_h to do the opposite. The energy method can be used to compute the energy of a given setting of all variables.


Reference

For more information on RBMs, see Geoffrey E. Hinton (2007) Boltzmann machine. Scholarpedia, 2(5):1668

The network is trained by Contrastive Divergence, as described in Hinton, G. E. (2002). Training products of experts by minimizing contrastive divergence. Neural Computation, 14(8):1711-1800

Variables:
  • w – Generative weights between hidden and observed variables.
  • bv – Bias vector of the observed variables.
  • bh – Bias vector of the hidden variables.

Full API documentation: RBMNode

class mdp.nodes.RBMWithLabelsNode

Restricted Boltzmann Machine with softmax labels. An RBM is an undirected probabilistic network with binary variables. In this case, the node is partitioned into a set of observed (visible) variables, a set of hidden (latent) variables, and a set of label variables (also observed), only one of which is active at any time. The node is able to learn associations between the visible variables and the labels. By default, the execute method returns the probability of one of the hiden variables being equal to 1 given the input. Use the sample_v method to sample from the observed variables (visible and labels) given a setting of the hidden variables, and sample_h to do the opposite. The energy method can be used to compute the energy of a given setting of all variables.


Reference

The network is trained by Contrastive Divergence, as described in Hinton, G. E. (2002). Training products of experts by minimizing contrastive divergence. Neural Computation, 14(8):1711-1800

For more information on RBMs with labels, see:

  • Geoffrey E. Hinton (2007) Boltzmann machine. Scholarpedia, 2(5):1668.
  • Hinton, G. E, Osindero, S., and Teh, Y. W. (2006). A fast learning algorithm for deep belief nets. Neural Computation, 18:1527-1554.
Variables:
  • w – Generative weights between hidden and observed variables.
  • bv – Bias vector of the observed variables.
  • bh – Bias vector of the hidden variables.

Full API documentation: RBMWithLabelsNode

class mdp.nodes.GrowingNeuralGasNode

Learn the topological structure of the input data by building a corresponding graph approximation.

The algorithm expands on the original Neural Gas algorithm (see mdp.nodes NeuralGasNode) in that the algorithm adds new nodes are added to the graph as more data becomes available. Im this way, if the growth rate is appropriate, one can avoid overfitting or underfitting the data.

Variables:graph – The corresponding mdp.graph.Graph object.

Reference

More information about the Growing Neural Gas algorithm can be found in B. Fritzke, A Growing Neural Gas Network Learns Topologies, in G. Tesauro, D. S. Touretzky, and T. K. Leen (editors), Advances in Neural Information Processing Systems 7, pages 625-632. MIT Press, Cambridge MA, 1995.

Full API documentation: GrowingNeuralGasNode

class mdp.nodes.LLENode

Perform a Locally Linear Embedding analysis on the data.

Variables:
  • training_projection – The LLE projection of the training data (defined when training finishes).
  • desired_variance – Variance limit used to compute intrinsic dimensionality.

Based on the algorithm outlined in An Introduction to Locally Linear Embedding by L. Saul and S. Roweis, using improvements suggested in Locally Linear Embedding for Classification by D. deRidder and R.P.W. Duin.


Reference

Roweis, S. and Saul, L., Nonlinear dimensionality reduction by locally linear embedding, Science 290 (5500), pp. 2323-2326, 2000.

Original code contributed by: Jake VanderPlas, University of Washington,

Full API documentation: LLENode

class mdp.nodes.HLLENode

Perform a Hessian Locally Linear Embedding analysis on the data.

Variables:
  • training_projection – The HLLE projection of the training data (defined when training finishes).
  • desired_variance – Variance limit used to compute intrinsic dimensionality.

Note

Many methods are inherited from LLENode, including _execute(), _adjust_output_dim(), etc. The main advantage of the Hessian estimator is to limit distortions of the input manifold. Once the model has been trained, it is sufficient (and much less computationally intensive) to determine projections for new points using the LLE framework.


Reference

Implementation based on algorithm outlined in Donoho, D. L., and Grimes, C., Hessian Eigenmaps: new locally linear embedding techniques for high-dimensional data, Proceedings of the National Academy of Sciences 100(10): 5591-5596, 2003.

Original code contributed by: Jake Vanderplas, University of Washington

Full API documentation: HLLENode

class mdp.nodes.LinearRegressionNode

Compute least-square, multivariate linear regression on the input data, i.e., learn coefficients b_j so that the linear combination y_i = b_0 + b_1 x_1 + ... b_N x_N , for i = 1 ... M, minimizes the sum of squared error given the training x’s and y’s.

This is a supervised learning node, and requires input data x and target data y to be supplied during training (see train docstring).

Variables:beta – The coefficients of the linear regression.

Full API documentation: LinearRegressionNode

class mdp.nodes.QuadraticExpansionNode

Perform expansion in the space formed by all linear and quadratic monomials. QuadraticExpansionNode() is equivalent to a PolynomialExpansionNode(2)

Full API documentation: QuadraticExpansionNode

class mdp.nodes.PolynomialExpansionNode

Perform expansion in a polynomial space.

Full API documentation: PolynomialExpansionNode

class mdp.nodes.RBFExpansionNode

Expand input space with Gaussian Radial Basis Functions (RBFs).

The input data is filtered through a set of unnormalized Gaussian filters, i.e.:

y_j = exp(-0.5/s_j * ||x - c_j||^2)

for isotropic RBFs, or more in general:

y_j = exp(-0.5 * (x-c_j)^T S^-1 (x-c_j))

for anisotropic RBFs.

Full API documentation: RBFExpansionNode

class mdp.nodes.GeneralExpansionNode

Expands the input samples by applying to them one or more functions provided.

The functions to be applied are specified by a list [f_0, …, f_k], where f_i, for 0 <= i <= k, denotes a particular function. The input data given to these functions is a two-dimensional array and the output is another two-dimensional array. The dimensionality of the output should depend only on the dimensionality of the input. Given a two-dimensional input array x, the output of the node is then [f_0(x), …, f_k(x)], that is, the concatenation of each one of the computed arrays f_i(x).

This node has been designed to facilitate nonlinear, fixed but arbitrary transformations of the data samples within MDP flows.

Original code contributed by Alberto Escalante.


Example

>>> import mdp
>>> from mdp import numx
>>> def identity(x): return x
>>> def u3(x): return numx.absolute(x)**3 #A simple nonlinear transformation
>>> def norm2(x): #Computes the norm of each sample returning an Nx1 array
>>>     return ((x**2).sum(axis=1)**0.5).reshape((-1,1)) 
>>> x = numx.array([[-2., 2.], [0.2, 0.3], [0.6, 1.2]])
>>> gen = mdp.nodes.GeneralExpansionNode(funcs=[identity, u3, norm2])
>>> print(gen.execute(x))
>>> [[-2.          2.          8.          8.          2.82842712]
>>>  [ 0.2         0.3         0.008       0.027       0.36055513]
>>>  [ 0.6         1.2         0.216       1.728       1.34164079]]

Full API documentation: GeneralExpansionNode

class mdp.nodes.GrowingNeuralGasExpansionNode

Perform a trainable radial basis expansion, where the centers and sizes of the basis functions are learned through a growing neural gas.

The positions of RBFs correspond to position of the nodes of the neural gas The sizes of the RBFs correspond to mean distance to the neighbouring nodes.


Note

Adjust the maximum number of nodes to control the dimension of the expansion.


Reference

More information on this expansion type can be found in: B. Fritzke. Growing cell structures-a self-organizing network for unsupervised and supervised learning. Neural Networks 7, p. 1441–1460 (1994).

Full API documentation: GrowingNeuralGasExpansionNode

class mdp.nodes.NeuralGasNode

Learn the topological structure of the input data by building a corresponding graph approximation (original Neural Gas algorithm).

Variables:
  • graph – The corresponding mdp.graph.Graph object.
  • max_epochs – Maximum number of epochs until which to train.

Reference

The Neural Gas algorithm was originally published in Martinetz, T. and Schulten, K.: A “Neural-Gas” Network Learns Topologies. In Kohonen, T., Maekisara, K., Simula, O., and Kangas, J. (eds.), Artificial Neural Networks. Elsevier, North-Holland., 1991.

Full API documentation: NeuralGasNode

class mdp.nodes.SignumClassifier

This classifier node classifies as 1 if the sum of the data points is positive and as -1 if the data point is negative.

Full API documentation: SignumClassifier

class mdp.nodes.PerceptronClassifier

A simple perceptron with input_dim input nodes.

Full API documentation: PerceptronClassifier

class mdp.nodes.SimpleMarkovClassifier

A simple version of a Markov classifier.

It can be trained on a vector of tuples the label being the next element in the testing data.

Full API documentation: SimpleMarkovClassifier

class mdp.nodes.DiscreteHopfieldClassifier

Node for simulating a simple discrete Hopfield model

Full API documentation: DiscreteHopfieldClassifier

class mdp.nodes.KMeansClassifier

Employs K-Means Clustering for a given number of centroids.

Full API documentation: KMeansClassifier

class mdp.nodes.NormalizeNode

Make input signal meanfree and unit variance.

Full API documentation: NormalizeNode

class mdp.nodes.GaussianClassifier

Perform a supervised Gaussian classification.

Given a set of labelled data, the node fits a gaussian distribution to each class.

Full API documentation: GaussianClassifier

class mdp.nodes.NearestMeanClassifier

Nearest-Mean classifier.

Full API documentation: NearestMeanClassifier

class mdp.nodes.KNNClassifier

K-Nearest-Neighbour Classifier.

Full API documentation: KNNClassifier

class mdp.nodes.EtaComputerNode

Compute the eta values of the normalized training data.

The delta value of a signal is a measure of its temporal variation, and is defined as the mean of the derivative squared, i.e. delta(x) = mean(dx/dt(t)^2). delta(x) is zero if x is a constant signal, and increases if the temporal variation of the signal is bigger.

The eta value is a more intuitive measure of temporal variation, defined as:

eta(x) = T/(2*pi) * sqrt(delta(x))

If x is a signal of length T which consists of a sine function that accomplishes exactly N oscillations, then eta(x)=N.

EtaComputerNode normalizes the training data to have unit variance, such that it is possible to compare the temporal variation of two signals independently from their scaling.

Note

  • If a data chunk is tlen data points long, this node is going to consider only the first tlen-1 points together with their derivatives. This means in particular that the variance of the signal is not computed on all data points. This behavior is compatible with that of SFANode.
  • This is an analysis node, i.e. the data is analyzed during training and the results are stored internally. Use the method get_eta to access them.

Reference

Wiskott, L. and Sejnowski, T.J. (2002). Slow Feature Analysis: Unsupervised Learning of Invariances, Neural Computation, 14(4):715-770.

Full API documentation: EtaComputerNode

class mdp.nodes.HitParadeNode

Collect the first n local maxima and minima of the training signal which are separated by a minimum gap d.

This is an analysis node, i.e. the data is analyzed during training and the results are stored internally. Use the get_maxima and get_minima methods to access them.

Full API documentation: HitParadeNode

class mdp.nodes.NoiseNode

Inject multiplicative or additive noise into the input data.

Original code contributed by Mathias Franzius.

Full API documentation: NoiseNode

class mdp.nodes.NormalNoiseNode

Special version of NoiseNode for Gaussian additive noise.

Unlike NoiseNode it does not store a noise function reference but simply uses numx_rand.normal.

Full API documentation: NormalNoiseNode

class mdp.nodes.TimeFramesNode

Copy delayed version of the input signal on the space dimensions.

For example, for time_frames=3 and gap=2:

[ X(1) Y(1)        [ X(1) Y(1) X(3) Y(3) X(5) Y(5)
  X(2) Y(2)          X(2) Y(2) X(4) Y(4) X(6) Y(6)
  X(3) Y(3)   -->    X(3) Y(3) X(5) Y(5) X(7) Y(7)
  X(4) Y(4)          X(4) Y(4) X(6) Y(6) X(8) Y(8)
  X(5) Y(5)          ...  ...  ...  ...  ...  ... ]
  X(6) Y(6)
  X(7) Y(7)
  X(8) Y(8)
  ...  ...  ]

It is not always possible to invert this transformation (the transformation is not surjective. However, the pseudo_inverse method does the correct thing when it is indeed possible.

Full API documentation: TimeFramesNode

class mdp.nodes.TimeDelayNode

Copy delayed version of the input signal on the space dimensions.

For example, for time_frames=3 and gap=2:

[ X(1) Y(1)        [ X(1) Y(1)   0    0    0    0
  X(2) Y(2)          X(2) Y(2)   0    0    0    0
  X(3) Y(3)   -->    X(3) Y(3) X(1) Y(1)   0    0
  X(4) Y(4)          X(4) Y(4) X(2) Y(2)   0    0
  X(5) Y(5)          X(5) Y(5) X(3) Y(3) X(1) Y(1)
  X(6) Y(6)          ...  ...  ...  ...  ...  ... ]
  X(7) Y(7)
  X(8) Y(8)
  ...  ...  ]

This node provides similar functionality as the TimeFramesNode, only that it performs a time embedding into the past rather than into the future.

See TimeDelaySlidingWindowNode for a sliding window delay node for application in a non-batch manner.

Original code contributed by Sebastian Hoefer. Dec 31, 2010

Full API documentation: TimeDelayNode

class mdp.nodes.TimeDelaySlidingWindowNode

TimeDelaySlidingWindowNode is an alternative to TimeDelayNode which should be used for online learning/execution. Whereas the TimeDelayNode works in a batch manner, for online application a sliding window is necessary which yields only one row per call.

Applied to the same data the collection of all returned rows of the TimeDelaySlidingWindowNode is equivalent to the result of the TimeDelayNode.

Original code contributed by Sebastian Hoefer. Dec 31, 2010

Full API documentation: TimeDelaySlidingWindowNode

class mdp.nodes.CutoffNode

Node to cut off values at specified bounds.

Works similar to numpy.clip, but also works when only a lower or upper bound is specified.

Full API documentation: CutoffNode

class mdp.nodes.AdaptiveCutoffNode

Node which uses the data history during training to learn cutoff values.

As opposed to the simple CutoffNode, a different cutoff value is learned for each data coordinate. For example if an upper cutoff fraction of 0.05 is specified, then the upper cutoff bound is set so that the upper 5% of the training data would have been clipped (in each dimension). The cutoff bounds are then applied during execution. This node also works as a HistogramNode, so the histogram data is stored.

When stop_training is called the cutoff values for each coordinate are calculated based on the collected histogram data.

Full API documentation: AdaptiveCutoffNode

class mdp.nodes.HistogramNode

Node which stores a history of the data during its training phase.

The data history is stored in self.data_hist and can also be deleted to free memory. Alternatively it can be automatically pickled to disk.

Note that data is only stored during training.

Full API documentation: HistogramNode

class mdp.nodes.IdentityNode

Execute returns the input data and the node is not trainable.

This node can be instantiated and is for example useful in complex network layouts.

Full API documentation: IdentityNode

class mdp.nodes.OnlineCenteringNode

OnlineCenteringNode centers the input data, that is, subtracts the arithmetic mean (average) from the input data. This is an online learnable node.

Note

The node’s train method updates the average (avg) according to the update rule:

avg <- (1 / n) * x + (1-1/n) * avg, where n is the total number of samples observed while training.

The node’s execute method subtracts the updated average from the input and returns it.

This node also supports centering via an exponentially weighted moving average that resembles a leaky integrator:

avg <- alpha * x + (1-alpha) * avg, where alpha = 2. / (avg_n + 1).

avg_n intuitively denotes a “window size”. For a large avg_n, ‘avg_n’-samples represent about 86% of the total weight.

Variables:avg – The updated average of the input data.

Full API documentation: OnlineCenteringNode

class mdp.nodes.OnlineTimeDiffNode

Compute the discrete time derivative of the input using backward difference approximation:

dx(n) = x(n) - x(n-1), where n is the total number of input samples observed during training.

This is an online learnable node that uses a buffer to store the previous input sample = x(n-1). The node’s train method updates the buffer. The node’s execute method returns the time difference using the stored buffer as its previous input sample x(n-1).

This node supports both “incremental” and “batch” training types.


Example

If the training and execute methods are called sample by sample incrementally::
train(x[1]), y[1]=execute(x[1]), train(x[2]), y[2]=execute(x[2]), …,
then::
y[1] = x[1] y[2] = x[2] - x[1] y[3] = x[3] - x[2] …
If training and execute methods are called block by block::
train([x[1], x[2], x[3]]), [y[3], y[4], y[5]] = execute([x[3], x[4], x[5]])
then::
y[3] = x[3] - x[2] y[4] = x[4] - x[3] y[5] = x[5] - x[4]

Note that the stored buffer is still = x[2]. Only train() method changes the state of the node. execute’s input data is always assumed to start at get_current_train_iteration() time step.

Full API documentation: OnlineTimeDiffNode

class mdp.nodes.CCIPCANode

Candid-Covariance free Incremental Principal Component Analysis (CCIPCA) extracts the principal components from the input data incrementally.

Variables:
  • v – Eigenvectors
  • d – Eigenvalues

Reference

More information about Candid-Covariance free Incremental Principal Component Analysis can be found in Weng J., Zhang Y. and Hwang W., Candid covariance-free incremental principal component analysis, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 25, 1034–1040, 2003.

Full API documentation: CCIPCANode

class mdp.nodes.CCIPCAWhiteningNode
Incrementally updates whitening vectors for the input data using CCIPCA.

Candid-Covariance free Incremental Principal Component Analysis (CCIPCA) extracts the principal components from the input data incrementally.

Variables:
  • v – Eigenvectors
  • d – Eigenvalues

Reference

More information about Candid-Covariance free Incremental Principal Component Analysis can be found in Weng J., Zhang Y. and Hwang W., Candid covariance-free incremental principal component analysis, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 25, 1034–1040, 2003.

Full API documentation: CCIPCAWhiteningNode

class mdp.nodes.MCANode

Minor Component Analysis (MCA) extracts minor components (dual of principal components) from the input data incrementally.

Variables:
  • v – Eigenvectors
  • d – Eigenvalues

Reference

More information about MCA can be found in Peng, D. and Yi, Z, A new algorithm for sequential minor component analysis, International Journal of Computational Intelligence Research, 2(2):207–215, 2006.

Full API documentation: MCANode

class mdp.nodes.IncSFANode

Incremental Slow Feature Analysis (IncSFA) extracts the slowly varying components from the input data incrementally.

Variables:
  • sf – Slow feature vectors
  • wv – Whitening vectors
  • sf_change – Difference in slow features after update

Reference

More information about IncSFA can be found in Kompella V.R, Luciw M. and Schmidhuber J., Incremental Slow Feature Analysis: Adaptive Low-Complexity Slow Feature Updating from High-Dimensional Input Streams, Neural Computation, 2012.

Full API documentation: IncSFANode

class mdp.nodes.RecursiveExpansionNode

Recursively computable (orthogonal) expansions.

Variables:
  • lower – The lower bound of the domain on which the recursion function is defined or orthogonal.
  • upper – The upper bound of the domain on which the recursion function is defined or orthogonal.

Full API documentation: RecursiveExpansionNode

class mdp.nodes.NormalizingRecursiveExpansionNode

Recursively computable (orthogonal) expansions and a trainable transformation to the domain of the expansions.

Variables:
  • lower – The lower bound of the domain on which the recursion function is defined or orthogonal.
  • upper – The upper bound of the domain on which the recursion function is defined or orthogonal.

Full API documentation: NormalizingRecursiveExpansionNode

class mdp.nodes.Convolution2DNode

Convolve input data with filter banks.

Convolution can be selected to be executed by linear filtering of the data, or in the frequency domain using a Discrete Fourier Transform.

Input data can be given as 3D data, each row being a 2D array to be convolved with the filters, or as 2D data, in which case the input_shape argument must be specified.

This node depends on scipy.

Variables:filters – Specifies a set of 2D filters that are convolved with the input data during execution.

Full API documentation: Convolution2DNode

class mdp.nodes.SGDRegressorScikitsLearnNode

Linear model fitted by minimizing a regularized empirical loss with SGD This node has been automatically generated by wrapping the sklearn.linear_model.stochastic_gradient.SGDRegressor class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. SGD stands for Stochastic Gradient Descent: the gradient of the loss is estimated each sample at a time and the model is updated along the way with a decreasing strength schedule (aka learning rate).

The regularizer is a penalty added to the loss function that shrinks model parameters towards the zero vector using either the squared euclidean norm L2 or the absolute norm L1 or a combination of both (Elastic Net). If the parameter update crosses the 0.0 value because of the regularizer, the update is truncated to 0.0 to allow for learning sparse models and achieve online feature selection.

This implementation works with data represented as dense numpy arrays of floating point values for the features.

Read more in the User Guide.

Parameters

loss : str, default: ‘squared_loss’

The loss function to be used. The possible values are ‘squared_loss’, ‘huber’, ‘epsilon_insensitive’, or ‘squared_epsilon_insensitive’

The ‘squared_loss’ refers to the ordinary least squares fit. ‘huber’ modifies ‘squared_loss’ to focus less on getting outliers correct by switching from squared to linear loss past a distance of epsilon. ‘epsilon_insensitive’ ignores errors less than epsilon and is linear past that; this is the loss function used in SVR. ‘squared_epsilon_insensitive’ is the same but becomes squared loss past a tolerance of epsilon.

penalty : str, ‘none’, ‘l2’, ‘l1’, or ‘elasticnet’
The penalty (aka regularization term) to be used. Defaults to ‘l2’ which is the standard regularizer for linear SVM models. ‘l1’ and ‘elasticnet’ might bring sparsity to the model (feature selection) not achievable with ‘l2’.
alpha : float
Constant that multiplies the regularization term. Defaults to 0.0001 Also used to compute learning_rate when set to ‘optimal’.
l1_ratio : float
The Elastic Net mixing parameter, with 0 <= l1_ratio <= 1. l1_ratio=0 corresponds to L2 penalty, l1_ratio=1 to L1. Defaults to 0.15.
fit_intercept : bool
Whether the intercept should be estimated or not. If False, the data is assumed to be already centered. Defaults to True.
max_iter : int, optional

The maximum number of passes over the training data (aka epochs). It only impacts the behavior in the fit method, and not the partial_fit. Defaults to 5. Defaults to 1000 from 0.21, or if tol is not None.

New in version 0.19.

tol : float or None, optional

The stopping criterion. If it is not None, the iterations will stop when (loss > previous_loss - tol). Defaults to None. Defaults to 1e-3 from 0.21.

New in version 0.19.

shuffle : bool, optional
Whether or not the training data should be shuffled after each epoch. Defaults to True.
verbose : integer, optional
The verbosity level.
epsilon : float
Epsilon in the epsilon-insensitive loss functions; only if loss is ‘huber’, ‘epsilon_insensitive’, or ‘squared_epsilon_insensitive’. For ‘huber’, determines the threshold at which it becomes less important to get the prediction exactly right. For epsilon-insensitive, any differences between the current prediction and the correct label are ignored if they are less than this threshold.
random_state : int, RandomState instance or None, optional (default=None)
The seed of the pseudo random number generator to use when shuffling the data. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.
learning_rate : string, optional

The learning rate schedule:

‘constant’:

  • eta = eta0

‘optimal’:

  • eta = 1.0 / (alpha * (t + t0))
  • where t0 is chosen by a heuristic proposed by Leon Bottou.
‘invscaling’: [default]
eta = eta0 / pow(t, power_t)

‘adaptive’:

  • eta = eta0, as long as the training keeps decreasing.
  • Each time n_iter_no_change consecutive epochs fail to decrease the
  • training loss by tol or fail to increase validation score by tol if
  • early_stopping is True, the current learning rate is divided by 5.
eta0 : double
The initial learning rate for the ‘constant’, ‘invscaling’ or ‘adaptive’ schedules. The default value is 0.0 as eta0 is not used by the default schedule ‘optimal’.
power_t : double
The exponent for inverse scaling learning rate [default 0.5].
early_stopping : bool, default=False

Whether to use early stopping to terminate training when validation score is not improving. If set to True, it will automatically set aside a fraction of training data as validation and terminate training when validation score is not improving by at least tol for n_iter_no_change consecutive epochs.

New in version 0.20.

validation_fraction : float, default=0.1

The proportion of training data to set aside as validation set for early stopping. Must be between 0 and 1. Only used if early_stopping is True.

New in version 0.20.

n_iter_no_change : int, default=5

Number of iterations with no improvement to wait before early stopping.

New in version 0.20.

warm_start : bool, optional

When set to True, reuse the solution of the previous call to fit as initialization, otherwise, just erase the previous solution. See the Glossary.

Repeatedly calling fit or partial_fit when warm_start is True can result in a different solution than when calling fit a single time because of the way the data is shuffled. If a dynamic learning rate is used, the learning rate is adapted depending on the number of samples already seen. Calling fit resets this counter, while partial_fit will result in increasing the existing counter.

average : bool or int, optional
When set to True, computes the averaged SGD weights and stores the result in the coef_ attribute. If set to an int greater than 1, averaging will begin once the total number of samples seen reaches average. So average=10 will begin averaging after seeing 10 samples.
n_iter : int, optional

The number of passes over the training data (aka epochs). Defaults to None. Deprecated, will be removed in 0.21.

Changed in version 0.19: Deprecated

Attributes

coef_ : array, shape (n_features,)
Weights assigned to the features.
intercept_ : array, shape (1,)
The intercept term.
average_coef_ : array, shape (n_features,)
Averaged weights assigned to the features.
average_intercept_ : array, shape (1,)
The averaged intercept term.
n_iter_ : int
The actual number of iterations to reach the stopping criterion.

Examples

>>> import numpy as np
>>> from sklearn import linear_model
>>> n_samples, n_features = 10, 5
>>> np.random.seed(0)
>>> y = np.random.randn(n_samples)
>>> X = np.random.randn(n_samples, n_features)
>>> clf = linear_model.SGDRegressor(max_iter=1000, tol=1e-3)
>>> clf.fit(X, y)
... 
SGDRegressor(alpha=0.0001, average=False, early_stopping=False,
       epsilon=0.1, eta0=0.01, fit_intercept=True, l1_ratio=0.15,
       learning_rate='invscaling', loss='squared_loss', max_iter=1000,
       n_iter=None, n_iter_no_change=5, penalty='l2', power_t=0.25,
       random_state=None, shuffle=True, tol=0.001, validation_fraction=0.1,
       verbose=0, warm_start=False)

See also

Ridge, ElasticNet, Lasso, sklearn.svm.SVR

Full API documentation: SGDRegressorScikitsLearnNode

class mdp.nodes.PatchExtractorScikitsLearnNode

Extracts patches from a collection of images This node has been automatically generated by wrapping the sklearn.feature_extraction.image.PatchExtractor class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Read more in the User Guide.

Parameters

patch_size : tuple of ints (patch_height, patch_width)
the dimensions of one patch
max_patches : integer or float, optional default is None
The maximum number of patches per image to extract. If max_patches is a float in (0, 1), it is taken to mean a proportion of the total number of patches.
random_state : int, RandomState instance or None, optional (default=None)
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.

Full API documentation: PatchExtractorScikitsLearnNode

class mdp.nodes.TheilSenRegressorScikitsLearnNode

Theil-Sen Estimator: robust multivariate regression model. This node has been automatically generated by wrapping the sklearn.linear_model.theil_sen.TheilSenRegressor class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. The algorithm calculates least square solutions on subsets with size n_subsamples of the samples in X. Any value of n_subsamples between the number of features and samples leads to an estimator with a compromise between robustness and efficiency. Since the number of least square solutions is “n_samples choose n_subsamples”, it can be extremely large and can therefore be limited with max_subpopulation. If this limit is reached, the subsets are chosen randomly. In a final step, the spatial median (or L1 median) is calculated of all least square solutions.

Read more in the User Guide.

Parameters

fit_intercept : boolean, optional, default True
Whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations.
copy_X : boolean, optional, default True
If True, X will be copied; else, it may be overwritten.
max_subpopulation : int, optional, default 1e4
Instead of computing with a set of cardinality ‘n choose k’, where n is the number of samples and k is the number of subsamples (at least number of features), consider only a stochastic subpopulation of a given maximal size if ‘n choose k’ is larger than max_subpopulation. For other than small problem sizes this parameter will determine memory usage and runtime if n_subsamples is not changed.
n_subsamples : int, optional, default None
Number of samples to calculate the parameters. This is at least the number of features (plus 1 if fit_intercept=True) and the number of samples as a maximum. A lower number leads to a higher breakdown point and a low efficiency while a high number leads to a low breakdown point and a high efficiency. If None, take the minimum number of subsamples leading to maximal robustness. If n_subsamples is set to n_samples, Theil-Sen is identical to least squares.
max_iter : int, optional, default 300
Maximum number of iterations for the calculation of spatial median.
tol : float, optional, default 1.e-3
Tolerance when calculating spatial median.
random_state : int, RandomState instance or None, optional, default None
A random number generator instance to define the state of the random permutations generator. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.
n_jobs : int or None, optional (default=None)
Number of CPUs to use during the cross validation. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
verbose : boolean, optional, default False
Verbose mode when fitting the model.

Attributes

coef_ : array, shape = (n_features)
Coefficients of the regression model (median of distribution).
intercept_ : float
Estimated intercept of regression model.
breakdown_ : float
Approximated breakdown point.
n_iter_ : int
Number of iterations needed for the spatial median.
n_subpopulation_ : int
Number of combinations taken into account from ‘n choose k’, where n is the number of samples and k is the number of subsamples.

Examples

>>> from sklearn.linear_model import TheilSenRegressor
>>> from sklearn.datasets import make_regression
>>> X, y = make_regression(
...     n_samples=200, n_features=2, noise=4.0, random_state=0)
>>> reg = TheilSenRegressor(random_state=0).fit(X, y)
>>> reg.score(X, y) 
0.9884...
>>> reg.predict(X[:1,])
array([-31.5871...])

References

Full API documentation: TheilSenRegressorScikitsLearnNode

class mdp.nodes.SparseRandomProjectionScikitsLearnNode

Reduce dimensionality through sparse random projection This node has been automatically generated by wrapping the sklearn.random_projection.SparseRandomProjection class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Sparse random matrix is an alternative to dense random projection matrix that guarantees similar embedding quality while being much more memory efficient and allowing faster computation of the projected data.

If we note s = 1 / density the components of the random matrix are drawn from:

  • -sqrt(s) / sqrt(n_components) with probability 1 / 2s
  • 0 with probability 1 - 1 / s
  • +sqrt(s) / sqrt(n_components) with probability 1 / 2s

Read more in the User Guide.

Parameters

n_components : int or ‘auto’, optional (default = ‘auto’)

Dimensionality of the target projection space.

n_components can be automatically adjusted according to the number of samples in the dataset and the bound given by the Johnson-Lindenstrauss lemma. In that case the quality of the embedding is controlled by the eps parameter.

It should be noted that Johnson-Lindenstrauss lemma can yield very conservative estimated of the required number of components as it makes no assumption on the structure of the dataset.

density : float in range ]0, 1], optional (default=’auto’)

Ratio of non-zero component in the random projection matrix.

If density = ‘auto’, the value is set to the minimum density as recommended by Ping Li et al.: 1 / sqrt(n_features).

Use density = 1 / 3.0 if you want to reproduce the results from Achlioptas, 2001.

eps : strictly positive float, optional, (default=0.1)

Parameter to control the quality of the embedding according to the Johnson-Lindenstrauss lemma when n_components is set to ‘auto’.

Smaller values lead to better embedding and higher number of dimensions (n_components) in the target projection space.

dense_output : boolean, optional (default=False)

If True, ensure that the output of the random projection is a dense numpy array even if the input and random projection matrix are both sparse. In practice, if the number of components is small the number of zero components in the projected data will be very small and it will be more CPU and memory efficient to use a dense representation.

If False, the projected data uses a sparse representation if the input is sparse.

random_state : int, RandomState instance or None, optional (default=None)
Control the pseudo random number generator used to generate the matrix at fit time. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.

Attributes

n_component_ : int
Concrete number of components computed when n_components=”auto”.
components_ : CSR matrix with shape [n_components, n_features]
Random matrix used for the projection.
density_ : float in range 0.0 - 1.0
Concrete density computed from when density = “auto”.

Examples

>>> import numpy as np
>>> from sklearn.random_projection import SparseRandomProjection
>>> np.random.seed(42)
>>> X = np.random.rand(100, 10000)
>>> transformer = SparseRandomProjection()
>>> X_new = transformer.fit_transform(X)
>>> X_new.shape
(100, 3947)
>>> # very few components are non-zero
>>> np.mean(transformer.components_ != 0) 
0.0100...

See Also

GaussianRandomProjection

References

[1]Ping Li, T. Hastie and K. W. Church, 2006, “Very Sparse Random Projections”. http://web.stanford.edu/~hastie/Papers/Ping/KDD06_rp.pdf
[2]D. Achlioptas, 2001, “Database-friendly random projections”, https://users.soe.ucsc.edu/~optas/papers/jl.pdf

Full API documentation: SparseRandomProjectionScikitsLearnNode

class mdp.nodes.LinearModelCVScikitsLearnNode

This node has been automatically generated by wrapping the sklearn.linear_model.coordinate_descent.LinearModelCV class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute.

Full API documentation: LinearModelCVScikitsLearnNode

class mdp.nodes.DictionaryLearningScikitsLearnNode

Dictionary learning This node has been automatically generated by wrapping the sklearn.decomposition.dict_learning.DictionaryLearning class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Finds a dictionary (a set of atoms) that can best be used to represent data using a sparse code.

Solves the optimization problem:

(U^*,V^*) = argmin 0.5 || Y - U V ||_2^2 + alpha * || U ||_1
            (U,V)
            with || V_k ||_2 = 1 for all  0 <= k < n_components

Read more in the User Guide.

Parameters

n_components : int,
number of dictionary elements to extract
alpha : float,
sparsity controlling parameter
max_iter : int,
maximum number of iterations to perform
tol : float,
tolerance for numerical error
fit_algorithm : {‘lars’, ‘cd’}

lars: uses the least angle regression method to solve the lasso problem (linear_model.lars_path) cd: uses the coordinate descent method to compute the Lasso solution (linear_model.Lasso). Lars will be faster if the estimated components are sparse.

New in version 0.17: cd coordinate descent method to improve speed.

transform_algorithm : {‘lasso_lars’, ‘lasso_cd’, ‘lars’, ‘omp’, ‘threshold’}

Algorithm used to transform the data lars: uses the least angle regression method (linear_model.lars_path) lasso_lars: uses Lars to compute the Lasso solution lasso_cd: uses the coordinate descent method to compute the Lasso solution (linear_model.Lasso). lasso_lars will be faster if the estimated components are sparse. omp: uses orthogonal matching pursuit to estimate the sparse solution threshold: squashes to zero all coefficients less than alpha from the projection dictionary * X'

New in version 0.17: lasso_cd coordinate descent method to improve speed.

transform_n_nonzero_coefs : int, 0.1 * n_features by default
Number of nonzero coefficients to target in each column of the solution. This is only used by algorithm=’lars’ and algorithm=’omp’ and is overridden by alpha in the omp case.
transform_alpha : float, 1. by default
If algorithm=’lasso_lars’ or algorithm=’lasso_cd’, alpha is the penalty applied to the L1 norm. If algorithm=’threshold’, alpha is the absolute value of the threshold below which coefficients will be squashed to zero. If algorithm=’omp’, alpha is the tolerance parameter: the value of the reconstruction error targeted. In this case, it overrides n_nonzero_coefs.
n_jobs : int or None, optional (default=None)
Number of parallel jobs to run. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
code_init : array of shape (n_samples, n_components),
initial value for the code, for warm restart
dict_init : array of shape (n_components, n_features),
initial values for the dictionary, for warm restart
verbose : bool, optional (default: False)
To control the verbosity of the procedure.
split_sign : bool, False by default
Whether to split the sparse feature vector into the concatenation of its negative part and its positive part. This can improve the performance of downstream classifiers.
random_state : int, RandomState instance or None, optional (default=None)
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.
positive_code : bool

Whether to enforce positivity when finding the code.

New in version 0.20.

positive_dict : bool

Whether to enforce positivity when finding the dictionary

New in version 0.20.

Attributes

components_ : array, [n_components, n_features]
dictionary atoms extracted from the data
error_ : array
vector of errors at each iteration
n_iter_ : int
Number of iterations run.

Notes

References:

J. Mairal, F. Bach, J. Ponce, G. Sapiro, 2009: Online dictionary learning for sparse coding (http://www.di.ens.fr/sierra/pdfs/icml09.pdf)

See also

SparseCoder MiniBatchDictionaryLearning SparsePCA MiniBatchSparsePCA

Full API documentation: DictionaryLearningScikitsLearnNode

class mdp.nodes.MinMaxScalerScikitsLearnNode

Transforms features by scaling each feature to a given range. This node has been automatically generated by wrapping the sklearn.preprocessing.data.MinMaxScaler class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. This estimator scales and translates each feature individually such that it is in the given range on the training set, e.g. between zero and one.

The transformation is given by:

X_std = (X - X.min(axis=0)) / (X.max(axis=0) - X.min(axis=0))
X_scaled = X_std * (max - min) + min

where min, max = feature_range.

The transformation is calculated as:

X_scaled = scale * X + min - X.min(axis=0) * scale
where scale = (max - min) / (X.max(axis=0) - X.min(axis=0))

This transformation is often used as an alternative to zero mean, unit variance scaling.

Read more in the User Guide.

Parameters

feature_range : tuple (min, max), default=(0, 1)
Desired range of transformed data.
copy : boolean, optional, default True
Set to False to perform inplace row normalization and avoid a copy (if the input is already a numpy array).

Attributes

min_ : ndarray, shape (n_features,)
Per feature adjustment for minimum. Equivalent to min - X.min(axis=0) * self.scale_
scale_ : ndarray, shape (n_features,)

Per feature relative scaling of the data. Equivalent to (max - min) / (X.max(axis=0) - X.min(axis=0))

New in version 0.17: scale_ attribute.

data_min_ : ndarray, shape (n_features,)

Per feature minimum seen in the data

New in version 0.17: data_min_

data_max_ : ndarray, shape (n_features,)

Per feature maximum seen in the data

New in version 0.17: data_max_

data_range_ : ndarray, shape (n_features,)

Per feature range (data_max_ - data_min_) seen in the data

New in version 0.17: data_range_

Examples

>>> from sklearn.preprocessing import MinMaxScaler
>>> data = [[-1, 2], [-0.5, 6], [0, 10], [1, 18]]
>>> scaler = MinMaxScaler()
>>> print(scaler.fit(data))
MinMaxScaler(copy=True, feature_range=(0, 1))
>>> print(scaler.data_max_)
[ 1. 18.]
>>> print(scaler.transform(data))
[[0.   0.  ]
 [0.25 0.25]
 [0.5  0.5 ]
 [1.   1.  ]]
>>> print(scaler.transform([[2, 2]]))
[[1.5 0. ]]

See also

minmax_scale: Equivalent function without the estimator API.

Notes

NaNs are treated as missing values: disregarded in fit, and maintained in transform.

For a comparison of the different scalers, transformers, and normalizers, see examples/preprocessing/plot_all_scaling.py.

Full API documentation: MinMaxScalerScikitsLearnNode

class mdp.nodes.ElasticNetCVScikitsLearnNode

Elastic Net model with iterative fitting along a regularization path. This node has been automatically generated by wrapping the sklearn.linear_model.coordinate_descent.ElasticNetCV class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. See glossary entry for cross-validation estimator.

Read more in the User Guide.

Parameters

l1_ratio : float or array of floats, optional
float between 0 and 1 passed to ElasticNet (scaling between l1 and l2 penalties). For l1_ratio = 0 the penalty is an L2 penalty. For l1_ratio = 1 it is an L1 penalty. For 0 < l1_ratio < 1, the penalty is a combination of L1 and L2 This parameter can be a list, in which case the different values are tested by cross-validation and the one giving the best prediction score is used. Note that a good choice of list of values for l1_ratio is often to put more values close to 1 (i.e. Lasso) and less close to 0 (i.e. Ridge), as in [.1, .5, .7, .9, .95, .99, 1]
eps : float, optional
Length of the path. eps=1e-3 means that alpha_min / alpha_max = 1e-3.
n_alphas : int, optional
Number of alphas along the regularization path, used for each l1_ratio.
alphas : numpy array, optional
List of alphas where to compute the models. If None alphas are set automatically
fit_intercept : boolean
whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (e.g. data is expected to be already centered).
normalize : boolean, optional, default False
This parameter is ignored when fit_intercept is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use sklearn.preprocessing.StandardScaler before calling fit on an estimator with normalize=False.
precompute : True | False | ‘auto’ | array-like
Whether to use a precomputed Gram matrix to speed up calculations. If set to 'auto' let us decide. The Gram matrix can also be passed as argument.
max_iter : int, optional
The maximum number of iterations
tol : float, optional
The tolerance for the optimization: if the updates are smaller than tol, the optimization code checks the dual gap for optimality and continues until it is smaller than tol.
cv : int, cross-validation generator or an iterable, optional

Determines the cross-validation splitting strategy. Possible inputs for cv are:

  • None, to use the default 3-fold cross-validation,
  • integer, to specify the number of folds.
  • CV splitter,
  • An iterable yielding (train, test) splits as arrays of indices.

For integer/None inputs, KFold is used.

Refer User Guide for the various cross-validation strategies that can be used here.

Changed in version 0.20: cv default value if None will change from 3-fold to 5-fold in v0.22.

copy_X : boolean, optional, default True
If True, X will be copied; else, it may be overwritten.
verbose : bool or integer
Amount of verbosity.
n_jobs : int or None, optional (default=None)
Number of CPUs to use during the cross validation. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
positive : bool, optional
When set to True, forces the coefficients to be positive.
random_state : int, RandomState instance or None, optional, default None
The seed of the pseudo random number generator that selects a random feature to update. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random. Used when selection == ‘random’.
selection : str, default ‘cyclic’
If set to ‘random’, a random coefficient is updated every iteration rather than looping over features sequentially by default. This (setting to ‘random’) often leads to significantly faster convergence especially when tol is higher than 1e-4.

Attributes

alpha_ : float
The amount of penalization chosen by cross validation
l1_ratio_ : float
The compromise between l1 and l2 penalization chosen by cross validation
coef_ : array, shape (n_features,) | (n_targets, n_features)
Parameter vector (w in the cost function formula),
intercept_ : float | array, shape (n_targets, n_features)
Independent term in the decision function.
mse_path_ : array, shape (n_l1_ratio, n_alpha, n_folds)
Mean square error for the test set on each fold, varying l1_ratio and alpha.
alphas_ : numpy array, shape (n_alphas,) or (n_l1_ratio, n_alphas)
The grid of alphas used for fitting, for each l1_ratio.
n_iter_ : int
number of iterations run by the coordinate descent solver to reach the specified tolerance for the optimal alpha.

Examples

>>> from sklearn.linear_model import ElasticNetCV
>>> from sklearn.datasets import make_regression
>>> X, y = make_regression(n_features=2, random_state=0)
>>> regr = ElasticNetCV(cv=5, random_state=0)
>>> regr.fit(X, y)
ElasticNetCV(alphas=None, copy_X=True, cv=5, eps=0.001, fit_intercept=True,
       l1_ratio=0.5, max_iter=1000, n_alphas=100, n_jobs=None,
       normalize=False, positive=False, precompute='auto', random_state=0,
       selection='cyclic', tol=0.0001, verbose=0)
>>> print(regr.alpha_) 
0.1994727942696716
>>> print(regr.intercept_) 
0.398...
>>> print(regr.predict([[0, 0]])) 
[0.398...]

Notes

For an example, see examples/linear_model/plot_lasso_model_selection.py.

To avoid unnecessary memory duplication the X argument of the fit method should be directly passed as a Fortran-contiguous numpy array.

The parameter l1_ratio corresponds to alpha in the glmnet R package while alpha corresponds to the lambda parameter in glmnet. More specifically, the optimization objective is:

1 / (2 * n_samples) * ||y - Xw||^2_2
+ alpha * l1_ratio * ||w||_1
+ 0.5 * alpha * (1 - l1_ratio) * ||w||^2_2

If you are interested in controlling the L1 and L2 penalty separately, keep in mind that this is equivalent to:

a * L1 + b * L2

for:

alpha = a + b and l1_ratio = a / (a + b).

See also

enet_path ElasticNet

Full API documentation: ElasticNetCVScikitsLearnNode

class mdp.nodes.RBFSamplerScikitsLearnNode

Approximates feature map of an RBF kernel by Monte Carlo approximation of its Fourier transform. This node has been automatically generated by wrapping the sklearn.kernel_approximation.RBFSampler class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. It implements a variant of Random Kitchen Sinks.[1]

Read more in the User Guide.

Parameters

gamma : float
Parameter of RBF kernel: exp(-gamma * x^2)
n_components : int
Number of Monte Carlo samples per original feature. Equals the dimensionality of the computed feature space.
random_state : int, RandomState instance or None, optional (default=None)
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.

Examples

>>> from sklearn.kernel_approximation import RBFSampler
>>> from sklearn.linear_model import SGDClassifier
>>> X = [[0, 0], [1, 1], [1, 0], [0, 1]]
>>> y = [0, 0, 1, 1]
>>> rbf_feature = RBFSampler(gamma=1, random_state=1)
>>> X_features = rbf_feature.fit_transform(X)
>>> clf = SGDClassifier(max_iter=5, tol=1e-3)
>>> clf.fit(X_features, y)
... 
SGDClassifier(alpha=0.0001, average=False, class_weight=None,
       early_stopping=False, epsilon=0.1, eta0=0.0, fit_intercept=True,
       l1_ratio=0.15, learning_rate='optimal', loss='hinge', max_iter=5,
       n_iter=None, n_iter_no_change=5, n_jobs=None, penalty='l2',
       power_t=0.5, random_state=None, shuffle=True, tol=0.001,
       validation_fraction=0.1, verbose=0, warm_start=False)
>>> clf.score(X_features, y)
1.0

Notes

See “Random Features for Large-Scale Kernel Machines” by A. Rahimi and Benjamin Recht.

[1] “Weighted Sums of Random Kitchen Sinks: Replacing minimization with randomization in learning” by A. Rahimi and Benjamin Recht. (http://people.eecs.berkeley.edu/~brecht/papers/08.rah.rec.nips.pdf)

Full API documentation: RBFSamplerScikitsLearnNode

class mdp.nodes.OrthogonalMatchingPursuitCVScikitsLearnNode

Cross-validated Orthogonal Matching Pursuit model (OMP). This node has been automatically generated by wrapping the sklearn.linear_model.omp.OrthogonalMatchingPursuitCV class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. See glossary entry for cross-validation estimator.

Read more in the User Guide.

Parameters

copy : bool, optional
Whether the design matrix X must be copied by the algorithm. A false value is only helpful if X is already Fortran-ordered, otherwise a copy is made anyway.
fit_intercept : boolean, optional
whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (e.g. data is expected to be already centered).
normalize : boolean, optional, default True
This parameter is ignored when fit_intercept is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use sklearn.preprocessing.StandardScaler before calling fit on an estimator with normalize=False.
max_iter : integer, optional
Maximum numbers of iterations to perform, therefore maximum features to include. 10% of n_features but at least 5 if available.
cv : int, cross-validation generator or an iterable, optional

Determines the cross-validation splitting strategy. Possible inputs for cv are:

  • None, to use the default 3-fold cross-validation,
  • integer, to specify the number of folds.
  • CV splitter,
  • An iterable yielding (train, test) splits as arrays of indices.

For integer/None inputs, KFold is used.

Refer User Guide for the various cross-validation strategies that can be used here.

Changed in version 0.20: cv default value if None will change from 3-fold to 5-fold in v0.22.

n_jobs : int or None, optional (default=None)
Number of CPUs to use during the cross validation. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
verbose : boolean or integer, optional
Sets the verbosity amount

Attributes

intercept_ : float or array, shape (n_targets,)
Independent term in decision function.
coef_ : array, shape (n_features,) or (n_targets, n_features)
Parameter vector (w in the problem formulation).
n_nonzero_coefs_ : int
Estimated number of non-zero coefficients giving the best mean squared error over the cross-validation folds.
n_iter_ : int or array-like
Number of active features across every target for the model refit with the best hyperparameters got by cross-validating across all folds.

Examples

>>> from sklearn.linear_model import OrthogonalMatchingPursuitCV
>>> from sklearn.datasets import make_regression
>>> X, y = make_regression(n_features=100, n_informative=10,
...                        noise=4, random_state=0)
>>> reg = OrthogonalMatchingPursuitCV(cv=5).fit(X, y)
>>> reg.score(X, y) 
0.9991...
>>> reg.n_nonzero_coefs_
10
>>> reg.predict(X[:1,])
array([-78.3854...])

See also

orthogonal_mp orthogonal_mp_gram lars_path Lars LassoLars OrthogonalMatchingPursuit LarsCV LassoLarsCV decomposition.sparse_encode

Full API documentation: OrthogonalMatchingPursuitCVScikitsLearnNode

class mdp.nodes.SkewedChi2SamplerScikitsLearnNode

Approximates feature map of the “skewed chi-squared” kernel by Monte Carlo approximation of its Fourier transform. This node has been automatically generated by wrapping the sklearn.kernel_approximation.SkewedChi2Sampler class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Read more in the User Guide.

Parameters

skewedness : float
“skewedness” parameter of the kernel. Needs to be cross-validated.
n_components : int
number of Monte Carlo samples per original feature. Equals the dimensionality of the computed feature space.
random_state : int, RandomState instance or None, optional (default=None)
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.

Examples

>>> from sklearn.kernel_approximation import SkewedChi2Sampler
>>> from sklearn.linear_model import SGDClassifier
>>> X = [[0, 0], [1, 1], [1, 0], [0, 1]]
>>> y = [0, 0, 1, 1]
>>> chi2_feature = SkewedChi2Sampler(skewedness=.01,
...                                  n_components=10,
...                                  random_state=0)
>>> X_features = chi2_feature.fit_transform(X, y)
>>> clf = SGDClassifier(max_iter=10, tol=1e-3)
>>> clf.fit(X_features, y)
SGDClassifier(alpha=0.0001, average=False, class_weight=None,
       early_stopping=False, epsilon=0.1, eta0=0.0, fit_intercept=True,
       l1_ratio=0.15, learning_rate='optimal', loss='hinge', max_iter=10,
       n_iter=None, n_iter_no_change=5, n_jobs=None, penalty='l2',
       power_t=0.5, random_state=None, shuffle=True, tol=0.001,
       validation_fraction=0.1, verbose=0, warm_start=False)
>>> clf.score(X_features, y)
1.0

References

See “Random Fourier Approximations for Skewed Multiplicative Histogram Kernels” by Fuxin Li, Catalin Ionescu and Cristian Sminchisescu.

See also

AdditiveChi2Sampler : A different approach for approximating an additive
variant of the chi squared kernel.

sklearn.metrics.pairwise.chi2_kernel : The exact chi squared kernel.

Full API documentation: SkewedChi2SamplerScikitsLearnNode

class mdp.nodes.RandomTreesEmbeddingScikitsLearnNode

An ensemble of totally random trees. This node has been automatically generated by wrapping the sklearn.ensemble.forest.RandomTreesEmbedding class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. An unsupervised transformation of a dataset to a high-dimensional sparse representation. A datapoint is coded according to which leaf of each tree it is sorted into. Using a one-hot encoding of the leaves, this leads to a binary coding with as many ones as there are trees in the forest.

The dimensionality of the resulting representation is n_out <= n_estimators * max_leaf_nodes. If max_leaf_nodes == None, the number of leaf nodes is at most n_estimators * 2 ** max_depth.

Read more in the User Guide.

Parameters

n_estimators : integer, optional (default=10)

Number of trees in the forest.

Changed in version 0.20: The default value of n_estimators will change from 10 in version 0.20 to 100 in version 0.22.

max_depth : integer, optional (default=5)
The maximum depth of each tree. If None, then nodes are expanded until all leaves are pure or until all leaves contain less than min_samples_split samples.
min_samples_split : int, float, optional (default=2)

The minimum number of samples required to split an internal node:

  • If int, then consider min_samples_split as the minimum number.
  • If float, then min_samples_split is a fraction and ceil(min_samples_split * n_samples) is the minimum number of samples for each split.

Changed in version 0.18: Added float values for fractions.

min_samples_leaf : int, float, optional (default=1)

The minimum number of samples required to be at a leaf node. A split point at any depth will only be considered if it leaves at least min_samples_leaf training samples in each of the left and right branches. This may have the effect of smoothing the model, especially in regression.

  • If int, then consider min_samples_leaf as the minimum number.
  • If float, then min_samples_leaf is a fraction and ceil(min_samples_leaf * n_samples) is the minimum number of samples for each node.

Changed in version 0.18: Added float values for fractions.

min_weight_fraction_leaf : float, optional (default=0.)
The minimum weighted fraction of the sum total of weights (of all the input samples) required to be at a leaf node. Samples have equal weight when sample_weight is not provided.
max_leaf_nodes : int or None, optional (default=None)
Grow trees with max_leaf_nodes in best-first fashion. Best nodes are defined as relative reduction in impurity. If None then unlimited number of leaf nodes.
min_impurity_decrease : float, optional (default=0.)

A node will be split if this split induces a decrease of the impurity greater than or equal to this value.

The weighted impurity decrease equation is the following:

N_t / N * (impurity - N_t_R / N_t * right_impurity
                    - N_t_L / N_t * left_impurity)

where N is the total number of samples, N_t is the number of samples at the current node, N_t_L is the number of samples in the left child, and N_t_R is the number of samples in the right child.

N, N_t, N_t_R and N_t_L all refer to the weighted sum, if sample_weight is passed.

New in version 0.19.

min_impurity_split : float, (default=1e-7)

Threshold for early stopping in tree growth. A node will split if its impurity is above the threshold, otherwise it is a leaf.

Deprecated since version 0.19: min_impurity_split has been deprecated in favor of min_impurity_decrease in 0.19. The default value of min_impurity_split will change from 1e-7 to 0 in 0.23 and it will be removed in 0.25. Use min_impurity_decrease instead.

sparse_output : bool, optional (default=True)
Whether or not to return a sparse CSR matrix, as default behavior, or to return a dense array compatible with dense pipeline operators.
n_jobs : int or None, optional (default=None)
The number of jobs to run in parallel for both fit and predict. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
random_state : int, RandomState instance or None, optional (default=None)
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.
verbose : int, optional (default=0)
Controls the verbosity when fitting and predicting.
warm_start : bool, optional (default=False)
When set to True, reuse the solution of the previous call to fit and add more estimators to the ensemble, otherwise, just fit a whole new forest. See the Glossary.

Attributes

estimators_ : list of DecisionTreeClassifier
The collection of fitted sub-estimators.

References

[1]P. Geurts, D. Ernst., and L. Wehenkel, “Extremely randomized trees”, Machine Learning, 63(1), 3-42, 2006.
[2]Moosmann, F. and Triggs, B. and Jurie, F. “Fast discriminative visual codebooks using randomized clustering forests” NIPS 2007

Full API documentation: RandomTreesEmbeddingScikitsLearnNode

class mdp.nodes.PerceptronScikitsLearnNode

Perceptron This node has been automatically generated by wrapping the sklearn.linear_model.perceptron.Perceptron class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Read more in the User Guide.

Parameters

penalty : None, ‘l2’ or ‘l1’ or ‘elasticnet’
The penalty (aka regularization term) to be used. Defaults to None.
alpha : float
Constant that multiplies the regularization term if regularization is used. Defaults to 0.0001
fit_intercept : bool
Whether the intercept should be estimated or not. If False, the data is assumed to be already centered. Defaults to True.
max_iter : int, optional

The maximum number of passes over the training data (aka epochs). It only impacts the behavior in the fit method, and not the partial_fit. Defaults to 5. Defaults to 1000 from 0.21, or if tol is not None.

New in version 0.19.

tol : float or None, optional

The stopping criterion. If it is not None, the iterations will stop when (loss > previous_loss - tol). Defaults to None. Defaults to 1e-3 from 0.21.

New in version 0.19.

shuffle : bool, optional, default True
Whether or not the training data should be shuffled after each epoch.
verbose : integer, optional
The verbosity level
eta0 : double
Constant by which the updates are multiplied. Defaults to 1.
n_jobs : int or None, optional (default=None)
The number of CPUs to use to do the OVA (One Versus All, for multi-class problems) computation. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
random_state : int, RandomState instance or None, optional, default None
The seed of the pseudo random number generator to use when shuffling the data. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.
early_stopping : bool, default=False

Whether to use early stopping to terminate training when validation. score is not improving. If set to True, it will automatically set aside a fraction of training data as validation and terminate training when validation score is not improving by at least tol for n_iter_no_change consecutive epochs.

New in version 0.20.

validation_fraction : float, default=0.1

The proportion of training data to set aside as validation set for early stopping. Must be between 0 and 1. Only used if early_stopping is True.

New in version 0.20.

n_iter_no_change : int, default=5

Number of iterations with no improvement to wait before early stopping.

New in version 0.20.

class_weight : dict, {class_label: weight} or “balanced” or None, optional

Preset for the class_weight fit parameter.

Weights associated with classes. If not given, all classes are supposed to have weight one.

The “balanced” mode uses the values of y to automatically adjust weights inversely proportional to class frequencies in the input data as n_samples / (n_classes * np.bincount(y))

warm_start : bool, optional
When set to True, reuse the solution of the previous call to fit as initialization, otherwise, just erase the previous solution. See the Glossary.
n_iter : int, optional

The number of passes over the training data (aka epochs). Defaults to None. Deprecated, will be removed in 0.21.

Changed in version 0.19: Deprecated

Attributes

coef_ : array, shape = [1, n_features] if n_classes == 2 else [n_classes, n_features]
Weights assigned to the features.
intercept_ : array, shape = [1] if n_classes == 2 else [n_classes]
Constants in decision function.
n_iter_ : int
The actual number of iterations to reach the stopping criterion. For multiclass fits, it is the maximum over every binary fit.

Notes

Perceptron is a classification algorithm which shares the same underlying implementation with SGDClassifier. In fact, Perceptron() is equivalent to SGDClassifier(loss=”perceptron”, eta0=1, learning_rate=”constant”, penalty=None).

Examples

>>> from sklearn.datasets import load_digits
>>> from sklearn.linear_model import Perceptron
>>> X, y = load_digits(return_X_y=True)
>>> clf = Perceptron(tol=1e-3, random_state=0)
>>> clf.fit(X, y)
Perceptron(alpha=0.0001, class_weight=None, early_stopping=False, eta0=1.0,
      fit_intercept=True, max_iter=None, n_iter=None, n_iter_no_change=5,
      n_jobs=None, penalty=None, random_state=0, shuffle=True, tol=0.001,
      validation_fraction=0.1, verbose=0, warm_start=False)
>>> clf.score(X, y) 
0.946...

See also

SGDClassifier

References

https://en.wikipedia.org/wiki/Perceptron and references therein.

Full API documentation: PerceptronScikitsLearnNode

class mdp.nodes.RidgeClassifierScikitsLearnNode

Classifier using Ridge regression. This node has been automatically generated by wrapping the sklearn.linear_model.ridge.RidgeClassifier class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Read more in the User Guide.

Parameters

alpha : float
Regularization strength; must be a positive float. Regularization improves the conditioning of the problem and reduces the variance of the estimates. Larger values specify stronger regularization. Alpha corresponds to C^-1 in other linear models such as LogisticRegression or LinearSVC.
fit_intercept : boolean
Whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (e.g. data is expected to be already centered).
normalize : boolean, optional, default False
This parameter is ignored when fit_intercept is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use sklearn.preprocessing.StandardScaler before calling fit on an estimator with normalize=False.
copy_X : boolean, optional, default True
If True, X will be copied; else, it may be overwritten.
max_iter : int, optional
Maximum number of iterations for conjugate gradient solver. The default value is determined by scipy.sparse.linalg.
tol : float
Precision of the solution.
class_weight : dict or ‘balanced’, optional

Weights associated with classes in the form {class_label: weight}. If not given, all classes are supposed to have weight one.

The “balanced” mode uses the values of y to automatically adjust weights inversely proportional to class frequencies in the input data as n_samples / (n_classes * np.bincount(y))

solver : {‘auto’, ‘svd’, ‘cholesky’, ‘lsqr’, ‘sparse_cg’, ‘sag’, ‘saga’}

Solver to use in the computational routines:

  • ‘auto’ chooses the solver automatically based on the type of data.

  • ‘svd’ uses a Singular Value Decomposition of X to compute the Ridge coefficients. More stable for singular matrices than ‘cholesky’.

  • ‘cholesky’ uses the standard scipy.linalg.solve function to obtain a closed-form solution.

  • ‘sparse_cg’ uses the conjugate gradient solver as found in scipy.sparse.linalg.cg. As an iterative algorithm, this solver is more appropriate than ‘cholesky’ for large-scale data (possibility to set tol and max_iter).

  • ‘lsqr’ uses the dedicated regularized least-squares routine scipy.sparse.linalg.lsqr. It is the fastest and uses an iterative procedure.

  • ‘sag’ uses a Stochastic Average Gradient descent, and ‘saga’ uses its unbiased and more flexible version named SAGA. Both methods use an iterative procedure, and are often faster than other solvers when both n_samples and n_features are large. Note that ‘sag’ and ‘saga’ fast convergence is only guaranteed on features with approximately the same scale. You can preprocess the data with a scaler from sklearn.preprocessing.

    New in version 0.17: Stochastic Average Gradient descent solver.

    New in version 0.19: SAGA solver.

random_state : int, RandomState instance or None, optional, default None
The seed of the pseudo random number generator to use when shuffling the data. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random. Used when solver == ‘sag’.

Attributes

coef_ : array, shape (n_features,) or (n_classes, n_features)
Weight vector(s).
intercept_ : float | array, shape = (n_targets,)
Independent term in decision function. Set to 0.0 if fit_intercept = False.
n_iter_ : array or None, shape (n_targets,)
Actual number of iterations for each target. Available only for sag and lsqr solvers. Other solvers will return None.

Examples

>>> from sklearn.datasets import load_breast_cancer
>>> from sklearn.linear_model import RidgeClassifier
>>> X, y = load_breast_cancer(return_X_y=True)
>>> clf = RidgeClassifier().fit(X, y)
>>> clf.score(X, y) 
0.9595...

See also

Ridge : Ridge regression RidgeClassifierCV : Ridge classifier with built-in cross validation

Notes

For multi-class classification, n_class classifiers are trained in a one-versus-all approach. Concretely, this is implemented by taking advantage of the multi-variate response support in Ridge.

Full API documentation: RidgeClassifierScikitsLearnNode

class mdp.nodes.LinearSVRScikitsLearnNode

Linear Support Vector Regression. This node has been automatically generated by wrapping the sklearn.svm.classes.LinearSVR class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Similar to SVR with parameter kernel=’linear’, but implemented in terms of liblinear rather than libsvm, so it has more flexibility in the choice of penalties and loss functions and should scale better to large numbers of samples.

This class supports both dense and sparse input.

Read more in the User Guide.

Parameters

epsilon : float, optional (default=0.1)
Epsilon parameter in the epsilon-insensitive loss function. Note that the value of this parameter depends on the scale of the target variable y. If unsure, set epsilon=0.
tol : float, optional (default=1e-4)
Tolerance for stopping criteria.
C : float, optional (default=1.0)
Penalty parameter C of the error term. The penalty is a squared l2 penalty. The bigger this parameter, the less regularization is used.
loss : string, optional (default=’epsilon_insensitive’)
Specifies the loss function. The epsilon-insensitive loss (standard SVR) is the L1 loss, while the squared epsilon-insensitive loss (‘squared_epsilon_insensitive’) is the L2 loss.
fit_intercept : boolean, optional (default=True)
Whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (i.e. data is expected to be already centered).
intercept_scaling : float, optional (default=1)
When self.fit_intercept is True, instance vector x becomes [x, self.intercept_scaling], i.e. a “synthetic” feature with constant value equals to intercept_scaling is appended to the instance vector. The intercept becomes intercept_scaling * synthetic feature weight Note! the synthetic feature weight is subject to l1/l2 regularization as all other features. To lessen the effect of regularization on synthetic feature weight (and therefore on the intercept) intercept_scaling has to be increased.
dual : bool, (default=True)
Select the algorithm to either solve the dual or primal optimization problem. Prefer dual=False when n_samples > n_features.
verbose : int, (default=0)
Enable verbose output. Note that this setting takes advantage of a per-process runtime setting in liblinear that, if enabled, may not work properly in a multithreaded context.
random_state : int, RandomState instance or None, optional (default=None)
The seed of the pseudo random number generator to use when shuffling the data. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.
max_iter : int, (default=1000)
The maximum number of iterations to be run.

Attributes

coef_ : array, shape = [n_features] if n_classes == 2 else [n_classes, n_features]

Weights assigned to the features (coefficients in the primal problem). This is only available in the case of a linear kernel.

coef_ is a readonly property derived from raw_coef_ that follows the internal memory layout of liblinear.

intercept_ : array, shape = [1] if n_classes == 2 else [n_classes]
Constants in decision function.

Examples

>>> from sklearn.svm import LinearSVR
>>> from sklearn.datasets import make_regression
>>> X, y = make_regression(n_features=4, random_state=0)
>>> regr = LinearSVR(random_state=0, tol=1e-5)
>>> regr.fit(X, y)
LinearSVR(C=1.0, dual=True, epsilon=0.0, fit_intercept=True,
     intercept_scaling=1.0, loss='epsilon_insensitive', max_iter=1000,
     random_state=0, tol=1e-05, verbose=0)
>>> print(regr.coef_)
[16.35... 26.91... 42.30... 60.47...]
>>> print(regr.intercept_)
[-4.29...]
>>> print(regr.predict([[0, 0, 0, 0]]))
[-4.29...]

See also

LinearSVC
Implementation of Support Vector Machine classifier using the same library as this class (liblinear).
SVR

Implementation of Support Vector Machine regression using libsvm:

  • the kernel can be non-linear but its SMO algorithm does not
  • scale to large number of samples as LinearSVC does.
sklearn.linear_model.SGDRegressor
SGDRegressor can optimize the same cost function as LinearSVR by adjusting the penalty and loss parameters. In addition it requires less memory, allows incremental (online) learning, and implements various loss functions and regularization regimes.

Full API documentation: LinearSVRScikitsLearnNode

class mdp.nodes.OrdinalEncoderScikitsLearnNode

Encode categorical features as an integer array. This node has been automatically generated by wrapping the sklearn.preprocessing._encoders.OrdinalEncoder class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. The input to this transformer should be an array-like of integers or strings, denoting the values taken on by categorical (discrete) features. The features are converted to ordinal integers. This results in a single column of integers (0 to n_categories - 1) per feature.

Read more in the User Guide.

Parameters

categories : ‘auto’ or a list of lists/arrays of values.

Categories (unique values) per feature:

  • ‘auto’ : Determine categories automatically from the training data.
  • list : categories[i] holds the categories expected in the ith column. The passed categories should not mix strings and numeric values, and should be sorted in case of numeric values.

The used categories can be found in the categories_ attribute.

dtype : number type, default np.float64
Desired dtype of output.

Attributes

categories_ : list of arrays
The categories of each feature determined during fitting (in order of the features in X and corresponding with the output of transform).

Examples

Given a dataset with two features, we let the encoder find the unique values per feature and transform the data to an ordinal encoding.

>>> from sklearn.preprocessing import OrdinalEncoder
>>> enc = OrdinalEncoder()
>>> X = [['Male', 1], ['Female', 3], ['Female', 2]]
>>> enc.fit(X)
... 
OrdinalEncoder(categories='auto', dtype=<... 'numpy.float64'>)
>>> enc.categories_
[array(['Female', 'Male'], dtype=object), array([1, 2, 3], dtype=object)]
>>> enc.transform([['Female', 3], ['Male', 1]])
array([[0., 2.],
       [1., 0.]])
>>> enc.inverse_transform([[1, 0], [0, 1]])
array([['Male', 1],
       ['Female', 2]], dtype=object)

See also

sklearn.preprocessing.OneHotEncoder : performs a one-hot encoding of
categorical features.
sklearn.preprocessing.LabelEncoder : encodes target labels with values
between 0 and n_classes-1.

Full API documentation: OrdinalEncoderScikitsLearnNode

class mdp.nodes.QuadraticDiscriminantAnalysisScikitsLearnNode

Quadratic Discriminant Analysis This node has been automatically generated by wrapping the sklearn.discriminant_analysis.QuadraticDiscriminantAnalysis class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. A classifier with a quadratic decision boundary, generated by fitting class conditional densities to the data and using Bayes’ rule.

The model fits a Gaussian density to each class.

New in version 0.17: QuadraticDiscriminantAnalysis

Read more in the User Guide.

Parameters

priors : array, optional, shape = [n_classes]
Priors on classes
reg_param : float, optional
Regularizes the covariance estimate as (1-reg_param)*Sigma + reg_param*np.eye(n_features)
store_covariance : boolean

If True the covariance matrices are computed and stored in the self.covariance_ attribute.

New in version 0.17.

tol : float, optional, default 1.0e-4

Threshold used for rank estimation.

New in version 0.17.

store_covariances : boolean
Deprecated, use store_covariance.

Attributes

covariance_ : list of array-like, shape = [n_features, n_features]
Covariance matrices of each class.
means_ : array-like, shape = [n_classes, n_features]
Class means.
priors_ : array-like, shape = [n_classes]
Class priors (sum to 1).
rotations_ : list of arrays
For each class k an array of shape [n_features, n_k], with n_k = min(n_features, number of elements in class k) It is the rotation of the Gaussian distribution, i.e. its principal axis.
scalings_ : list of arrays
For each class k an array of shape [n_k]. It contains the scaling of the Gaussian distributions along its principal axes, i.e. the variance in the rotated coordinate system.

Examples

>>> from sklearn.discriminant_analysis import QuadraticDiscriminantAnalysis
>>> import numpy as np
>>> X = np.array([[-1, -1], [-2, -1], [-3, -2], [1, 1], [2, 1], [3, 2]])
>>> y = np.array([1, 1, 1, 2, 2, 2])
>>> clf = QuadraticDiscriminantAnalysis()
>>> clf.fit(X, y)
... 
QuadraticDiscriminantAnalysis(priors=None, reg_param=0.0,
                              store_covariance=False,
                              store_covariances=None, tol=0.0001)
>>> print(clf.predict([[-0.8, -1]]))
[1]

See also

sklearn.discriminant_analysis.LinearDiscriminantAnalysis: Linear
Discriminant Analysis

Full API documentation: QuadraticDiscriminantAnalysisScikitsLearnNode

class mdp.nodes.MLPClassifierScikitsLearnNode

Multi-layer Perceptron classifier. This node has been automatically generated by wrapping the sklearn.neural_network.multilayer_perceptron.MLPClassifier class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. This model optimizes the log-loss function using LBFGS or stochastic gradient descent.

New in version 0.18.

Parameters

hidden_layer_sizes : tuple, length = n_layers - 2, default (100,)
The ith element represents the number of neurons in the ith hidden layer.
activation : {‘identity’, ‘logistic’, ‘tanh’, ‘relu’}, default ‘relu’

Activation function for the hidden layer.

  • ‘identity’, no-op activation, useful to implement linear bottleneck, returns f(x) = x
  • ‘logistic’, the logistic sigmoid function, returns f(x) = 1 / (1 + exp(-x)).
  • ‘tanh’, the hyperbolic tan function, returns f(x) = tanh(x).
  • ‘relu’, the rectified linear unit function, returns f(x) = max(0, x)
solver : {‘lbfgs’, ‘sgd’, ‘adam’}, default ‘adam’

The solver for weight optimization.

  • ‘lbfgs’ is an optimizer in the family of quasi-Newton methods.
  • ‘sgd’ refers to stochastic gradient descent.
  • ‘adam’ refers to a stochastic gradient-based optimizer proposed by Kingma, Diederik, and Jimmy Ba

Note: The default solver ‘adam’ works pretty well on relatively large datasets (with thousands of training samples or more) in terms of both training time and validation score. For small datasets, however, ‘lbfgs’ can converge faster and perform better.

alpha : float, optional, default 0.0001
L2 penalty (regularization term) parameter.
batch_size : int, optional, default ‘auto’
Size of minibatches for stochastic optimizers. If the solver is ‘lbfgs’, the classifier will not use minibatch. When set to “auto”, batch_size=min(200, n_samples)
learning_rate : {‘constant’, ‘invscaling’, ‘adaptive’}, default ‘constant’

Learning rate schedule for weight updates.

  • ‘constant’ is a constant learning rate given by ‘learning_rate_init’.
  • ‘invscaling’ gradually decreases the learning rate at each time step ‘t’ using an inverse scaling exponent of ‘power_t’. effective_learning_rate = learning_rate_init / pow(t, power_t)
  • ‘adaptive’ keeps the learning rate constant to ‘learning_rate_init’ as long as training loss keeps decreasing. Each time two consecutive epochs fail to decrease training loss by at least tol, or fail to increase validation score by at least tol if ‘early_stopping’ is on, the current learning rate is divided by 5.

Only used when solver='sgd'.

learning_rate_init : double, optional, default 0.001
The initial learning rate used. It controls the step-size in updating the weights. Only used when solver=’sgd’ or ‘adam’.
power_t : double, optional, default 0.5
The exponent for inverse scaling learning rate. It is used in updating effective learning rate when the learning_rate is set to ‘invscaling’. Only used when solver=’sgd’.
max_iter : int, optional, default 200
Maximum number of iterations. The solver iterates until convergence (determined by ‘tol’) or this number of iterations. For stochastic solvers (‘sgd’, ‘adam’), note that this determines the number of epochs (how many times each data point will be used), not the number of gradient steps.
shuffle : bool, optional, default True
Whether to shuffle samples in each iteration. Only used when solver=’sgd’ or ‘adam’.
random_state : int, RandomState instance or None, optional, default None
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.
tol : float, optional, default 1e-4
Tolerance for the optimization. When the loss or score is not improving by at least tol for n_iter_no_change consecutive iterations, unless learning_rate is set to ‘adaptive’, convergence is considered to be reached and training stops.
verbose : bool, optional, default False
Whether to print progress messages to stdout.
warm_start : bool, optional, default False
When set to True, reuse the solution of the previous call to fit as initialization, otherwise, just erase the previous solution. See the Glossary.
momentum : float, default 0.9
Momentum for gradient descent update. Should be between 0 and 1. Only used when solver=’sgd’.
nesterovs_momentum : boolean, default True
Whether to use Nesterov’s momentum. Only used when solver=’sgd’ and momentum > 0.
early_stopping : bool, default False
Whether to use early stopping to terminate training when validation score is not improving. If set to true, it will automatically set aside 10% of training data as validation and terminate training when validation score is not improving by at least tol for n_iter_no_change consecutive epochs. Only effective when solver=’sgd’ or ‘adam’
validation_fraction : float, optional, default 0.1
The proportion of training data to set aside as validation set for early stopping. Must be between 0 and 1. Only used if early_stopping is True
beta_1 : float, optional, default 0.9
Exponential decay rate for estimates of first moment vector in adam, should be in [0, 1). Only used when solver=’adam’
beta_2 : float, optional, default 0.999
Exponential decay rate for estimates of second moment vector in adam, should be in [0, 1). Only used when solver=’adam’
epsilon : float, optional, default 1e-8
Value for numerical stability in adam. Only used when solver=’adam’
n_iter_no_change : int, optional, default 10

Maximum number of epochs to not meet tol improvement. Only effective when solver=’sgd’ or ‘adam’

New in version 0.20.

Attributes

classes_ : array or list of array of shape (n_classes,)
Class labels for each output.
loss_ : float
The current loss computed with the loss function.
coefs_ : list, length n_layers - 1
The ith element in the list represents the weight matrix corresponding to layer i.
intercepts_ : list, length n_layers - 1
The ith element in the list represents the bias vector corresponding to layer i + 1.
n_iter_ : int,
The number of iterations the solver has ran.
n_layers_ : int
Number of layers.
n_outputs_ : int
Number of outputs.
out_activation_ : string
Name of the output activation function.

Notes

MLPClassifier trains iteratively since at each time step the partial derivatives of the loss function with respect to the model parameters are computed to update the parameters.

It can also have a regularization term added to the loss function that shrinks model parameters to prevent overfitting.

This implementation works with data represented as dense numpy arrays or sparse scipy arrays of floating point values.

References

Hinton, Geoffrey E.
“Connectionist learning procedures.” Artificial intelligence 40.1 (1989): 185-234.
Glorot, Xavier, and Yoshua Bengio. “Understanding the difficulty of
training deep feedforward neural networks.” International Conference on Artificial Intelligence and Statistics. 2010.
He, Kaiming, et al. “Delving deep into rectifiers: Surpassing human-level
performance on imagenet classification.” arXiv preprint arXiv:1502.01852 (2015).
Kingma, Diederik, and Jimmy Ba. “Adam: A method for stochastic
optimization.” arXiv preprint arXiv:1412.6980 (2014).

Full API documentation: MLPClassifierScikitsLearnNode

class mdp.nodes.KNeighborsClassifierScikitsLearnNode

Classifier implementing the k-nearest neighbors vote. This node has been automatically generated by wrapping the sklearn.neighbors.classification.KNeighborsClassifier class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Read more in the User Guide.

Parameters

n_neighbors : int, optional (default = 5)
Number of neighbors to use by default for kneighbors() queries.
weights : str or callable, optional (default = ‘uniform’)

weight function used in prediction. Possible values:

  • ‘uniform’ : uniform weights. All points in each neighborhood are weighted equally.
  • ‘distance’ : weight points by the inverse of their distance. in this case, closer neighbors of a query point will have a greater influence than neighbors which are further away.
  • [callable] : a user-defined function which accepts an array of distances, and returns an array of the same shape containing the weights.
algorithm : {‘auto’, ‘ball_tree’, ‘kd_tree’, ‘brute’}, optional

Algorithm used to compute the nearest neighbors:

  • ‘ball_tree’ will use BallTree
  • ‘kd_tree’ will use KDTree
  • ‘brute’ will use a brute-force search.
  • ‘auto’ will attempt to decide the most appropriate algorithm based on the values passed to fit() method.

Note: fitting on sparse input will override the setting of this parameter, using brute force.

leaf_size : int, optional (default = 30)
Leaf size passed to BallTree or KDTree. This can affect the speed of the construction and query, as well as the memory required to store the tree. The optimal value depends on the nature of the problem.
p : integer, optional (default = 2)
Power parameter for the Minkowski metric. When p = 1, this is equivalent to using manhattan_distance (l1), and euclidean_distance (l2) for p = 2. For arbitrary p, minkowski_distance (l_p) is used.
metric : string or callable, default ‘minkowski’
the distance metric to use for the tree. The default metric is minkowski, and with p=2 is equivalent to the standard Euclidean metric. See the documentation of the DistanceMetric class for a list of available metrics.
metric_params : dict, optional (default = None)
Additional keyword arguments for the metric function.
n_jobs : int or None, optional (default=None)
The number of parallel jobs to run for neighbors search. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details. Doesn’t affect fit() method.

Examples

>>> X = [[0], [1], [2], [3]]
>>> y = [0, 0, 1, 1]
>>> from sklearn.neighbors import KNeighborsClassifier
>>> neigh = KNeighborsClassifier(n_neighbors=3)
>>> neigh.fit(X, y) 
KNeighborsClassifier(...)
>>> print(neigh.predict([[1.1]]))
[0]
>>> print(neigh.predict_proba([[0.9]]))
[[0.66666667 0.33333333]]

See also

RadiusNeighborsClassifier KNeighborsRegressor RadiusNeighborsRegressor NearestNeighbors

Notes

See Nearest Neighbors in the online documentation for a discussion of the choice of algorithm and leaf_size.

Warning

Regarding the Nearest Neighbors algorithms, if it is found that two neighbors, neighbor k+1 and k, have identical distances but different labels, the results will depend on the ordering of the training data.

https://en.wikipedia.org/wiki/K-nearest_neighbor_algorithm

Full API documentation: KNeighborsClassifierScikitsLearnNode

class mdp.nodes.PowerTransformerScikitsLearnNode

Apply a power transform featurewise to make data more Gaussian-like. This node has been automatically generated by wrapping the sklearn.preprocessing.data.PowerTransformer class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Power transforms are a family of parametric, monotonic transformations that are applied to make data more Gaussian-like. This is useful for modeling issues related to heteroscedasticity (non-constant variance), or other situations where normality is desired.

Currently, PowerTransformer supports the Box-Cox transform and the Yeo-Johnson transform. The optimal parameter for stabilizing variance and minimizing skewness is estimated through maximum likelihood.

Box-Cox requires input data to be strictly positive, while Yeo-Johnson supports both positive or negative data.

By default, zero-mean, unit-variance normalization is applied to the transformed data.

Read more in the User Guide.

Parameters

method : str, (default=’yeo-johnson’)

The power transform method. Available methods are:

  • ‘yeo-johnson’ [1]_, works with positive and negative values
  • ‘box-cox’ [2]_, only works with strictly positive values
standardize : boolean, default=True
Set to True to apply zero-mean, unit-variance normalization to the transformed output.
copy : boolean, optional, default=True
Set to False to perform inplace computation during transformation.

Attributes

lambdas_ : array of float, shape (n_features,)
The parameters of the power transformation for the selected features.

Examples

>>> import numpy as np
>>> from sklearn.preprocessing import PowerTransformer
>>> pt = PowerTransformer()
>>> data = [[1, 2], [3, 2], [4, 5]]
>>> print(pt.fit(data))
PowerTransformer(copy=True, method='yeo-johnson', standardize=True)
>>> print(pt.lambdas_)
[ 1.386... -3.100...]
>>> print(pt.transform(data))
[[-1.316... -0.707...]
 [ 0.209... -0.707...]
 [ 1.106...  1.414...]]

See also

power_transform : Equivalent function without the estimator API.

QuantileTransformer : Maps data to a standard normal distribution with
the parameter output_distribution=’normal’.

Notes

NaNs are treated as missing values: disregarded in fit, and maintained in transform.

For a comparison of the different scalers, transformers, and normalizers, see examples/preprocessing/plot_all_scaling.py.

References

[1]I.K. Yeo and R.A. Johnson, “A new family of power transformations to improve normality or symmetry.” Biometrika, 87(4), pp.954-959, (2000).
[2]G.E.P. Box and D.R. Cox, “An Analysis of Transformations”, Journal of the Royal Statistical Society B, 26, 211-252 (1964).

Full API documentation: PowerTransformerScikitsLearnNode

class mdp.nodes.SparsePCAScikitsLearnNode

Sparse Principal Components Analysis (SparsePCA) This node has been automatically generated by wrapping the sklearn.decomposition.sparse_pca.SparsePCA class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Finds the set of sparse components that can optimally reconstruct the data. The amount of sparseness is controllable by the coefficient of the L1 penalty, given by the parameter alpha.

Read more in the User Guide.

Parameters

n_components : int,
Number of sparse atoms to extract.
alpha : float,
Sparsity controlling parameter. Higher values lead to sparser components.
ridge_alpha : float,
Amount of ridge shrinkage to apply in order to improve conditioning when calling the transform method.
max_iter : int,
Maximum number of iterations to perform.
tol : float,
Tolerance for the stopping condition.
method : {‘lars’, ‘cd’}
lars: uses the least angle regression method to solve the lasso problem (linear_model.lars_path) cd: uses the coordinate descent method to compute the Lasso solution (linear_model.Lasso). Lars will be faster if the estimated components are sparse.
n_jobs : int or None, optional (default=None)
Number of parallel jobs to run. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
U_init : array of shape (n_samples, n_components),
Initial values for the loadings for warm restart scenarios.
V_init : array of shape (n_components, n_features),
Initial values for the components for warm restart scenarios.
verbose : int
Controls the verbosity; the higher, the more messages. Defaults to 0.
random_state : int, RandomState instance or None, optional (default=None)
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.
normalize_components : boolean, optional (default=False)
  • if False, use a version of Sparse PCA without components normalization and without data centering. This is likely a bug and even though it’s the default for backward compatibility, this should not be used.
  • if True, use a version of Sparse PCA with components normalization and data centering.

New in version 0.20.

Deprecated since version 0.22: normalize_components was added and set to False for backward compatibility. It would be set to True from 0.22 onwards.

Attributes

components_ : array, [n_components, n_features]
Sparse components extracted from the data.
error_ : array
Vector of errors at each iteration.
n_iter_ : int
Number of iterations run.
mean_ : array, shape (n_features,)
Per-feature empirical mean, estimated from the training set. Equal to X.mean(axis=0).

Examples

>>> import numpy as np
>>> from sklearn.datasets import make_friedman1
>>> from sklearn.decomposition import SparsePCA
>>> X, _ = make_friedman1(n_samples=200, n_features=30, random_state=0)
>>> transformer = SparsePCA(n_components=5,
...         normalize_components=True,
...         random_state=0)
>>> transformer.fit(X) 
SparsePCA(...)
>>> X_transformed = transformer.transform(X)
>>> X_transformed.shape
(200, 5)
>>> # most values in the ``components_`` are zero (sparsity)
>>> np.mean(transformer.components_ == 0) 
0.9666...

See also

PCA MiniBatchSparsePCA DictionaryLearning

Full API documentation: SparsePCAScikitsLearnNode

class mdp.nodes.ExtraTreeRegressorScikitsLearnNode

An extremely randomized tree regressor. This node has been automatically generated by wrapping the sklearn.tree.tree.ExtraTreeRegressor class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Extra-trees differ from classic decision trees in the way they are built. When looking for the best split to separate the samples of a node into two groups, random splits are drawn for each of the max_features randomly selected features and the best split among those is chosen. When max_features is set 1, this amounts to building a totally random decision tree.

Warning: Extra-trees should only be used within ensemble methods.

Read more in the User Guide.

Parameters

criterion : string, optional (default=”mse”)

The function to measure the quality of a split. Supported criteria are “mse” for the mean squared error, which is equal to variance reduction as feature selection criterion, and “mae” for the mean absolute error.

New in version 0.18: Mean Absolute Error (MAE) criterion.

splitter : string, optional (default=”random”)
The strategy used to choose the split at each node. Supported strategies are “best” to choose the best split and “random” to choose the best random split.
max_depth : int or None, optional (default=None)
The maximum depth of the tree. If None, then nodes are expanded until all leaves are pure or until all leaves contain less than min_samples_split samples.
min_samples_split : int, float, optional (default=2)

The minimum number of samples required to split an internal node:

  • If int, then consider min_samples_split as the minimum number.
  • If float, then min_samples_split is a fraction and ceil(min_samples_split * n_samples) are the minimum number of samples for each split.

Changed in version 0.18: Added float values for fractions.

min_samples_leaf : int, float, optional (default=1)

The minimum number of samples required to be at a leaf node. A split point at any depth will only be considered if it leaves at least min_samples_leaf training samples in each of the left and right branches. This may have the effect of smoothing the model, especially in regression.

  • If int, then consider min_samples_leaf as the minimum number.
  • If float, then min_samples_leaf is a fraction and ceil(min_samples_leaf * n_samples) are the minimum number of samples for each node.

Changed in version 0.18: Added float values for fractions.

min_weight_fraction_leaf : float, optional (default=0.)
The minimum weighted fraction of the sum total of weights (of all the input samples) required to be at a leaf node. Samples have equal weight when sample_weight is not provided.
max_features : int, float, string or None, optional (default=”auto”)

The number of features to consider when looking for the best split:

  • If int, then consider max_features features at each split.
  • If float, then max_features is a fraction and int(max_features * n_features) features are considered at each split.
  • If “auto”, then max_features=n_features.
  • If “sqrt”, then max_features=sqrt(n_features).
  • If “log2”, then max_features=log2(n_features).
  • If None, then max_features=n_features.

Note: the search for a split does not stop until at least one valid partition of the node samples is found, even if it requires to effectively inspect more than max_features features.

random_state : int, RandomState instance or None, optional (default=None)
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.
min_impurity_decrease : float, optional (default=0.)

A node will be split if this split induces a decrease of the impurity greater than or equal to this value.

The weighted impurity decrease equation is the following:

N_t / N * (impurity - N_t_R / N_t * right_impurity
                    - N_t_L / N_t * left_impurity)

where N is the total number of samples, N_t is the number of samples at the current node, N_t_L is the number of samples in the left child, and N_t_R is the number of samples in the right child.

N, N_t, N_t_R and N_t_L all refer to the weighted sum, if sample_weight is passed.

New in version 0.19.

min_impurity_split : float, (default=1e-7)

Threshold for early stopping in tree growth. A node will split if its impurity is above the threshold, otherwise it is a leaf.

Deprecated since version 0.19: min_impurity_split has been deprecated in favor of min_impurity_decrease in 0.19. The default value of min_impurity_split will change from 1e-7 to 0 in 0.23 and it will be removed in 0.25. Use min_impurity_decrease instead.

max_leaf_nodes : int or None, optional (default=None)
Grow a tree with max_leaf_nodes in best-first fashion. Best nodes are defined as relative reduction in impurity. If None then unlimited number of leaf nodes.

See also

ExtraTreeClassifier, sklearn.ensemble.ExtraTreesClassifier, sklearn.ensemble.ExtraTreesRegressor

Notes

The default values for the parameters controlling the size of the trees (e.g. max_depth, min_samples_leaf, etc.) lead to fully grown and unpruned trees which can potentially be very large on some data sets. To reduce memory consumption, the complexity and size of the trees should be controlled by setting those parameter values.

References

[1]P. Geurts, D. Ernst., and L. Wehenkel, “Extremely randomized trees”, Machine Learning, 63(1), 3-42, 2006.

Full API documentation: ExtraTreeRegressorScikitsLearnNode

class mdp.nodes.ExtraTreesClassifierScikitsLearnNode

An extra-trees classifier. This node has been automatically generated by wrapping the sklearn.ensemble.forest.ExtraTreesClassifier class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. This class implements a meta estimator that fits a number of randomized decision trees (a.k.a. extra-trees) on various sub-samples of the dataset and uses averaging to improve the predictive accuracy and control over-fitting.

Read more in the User Guide.

Parameters

n_estimators : integer, optional (default=10)

The number of trees in the forest.

Changed in version 0.20: The default value of n_estimators will change from 10 in version 0.20 to 100 in version 0.22.

criterion : string, optional (default=”gini”)
The function to measure the quality of a split. Supported criteria are “gini” for the Gini impurity and “entropy” for the information gain.
max_depth : integer or None, optional (default=None)
The maximum depth of the tree. If None, then nodes are expanded until all leaves are pure or until all leaves contain less than min_samples_split samples.
min_samples_split : int, float, optional (default=2)

The minimum number of samples required to split an internal node:

  • If int, then consider min_samples_split as the minimum number.
  • If float, then min_samples_split is a fraction and ceil(min_samples_split * n_samples) are the minimum number of samples for each split.

Changed in version 0.18: Added float values for fractions.

min_samples_leaf : int, float, optional (default=1)

The minimum number of samples required to be at a leaf node. A split point at any depth will only be considered if it leaves at least min_samples_leaf training samples in each of the left and right branches. This may have the effect of smoothing the model, especially in regression.

  • If int, then consider min_samples_leaf as the minimum number.
  • If float, then min_samples_leaf is a fraction and ceil(min_samples_leaf * n_samples) are the minimum number of samples for each node.

Changed in version 0.18: Added float values for fractions.

min_weight_fraction_leaf : float, optional (default=0.)
The minimum weighted fraction of the sum total of weights (of all the input samples) required to be at a leaf node. Samples have equal weight when sample_weight is not provided.
max_features : int, float, string or None, optional (default=”auto”)

The number of features to consider when looking for the best split:

  • If int, then consider max_features features at each split.
  • If float, then max_features is a fraction and int(max_features * n_features) features are considered at each split.
  • If “auto”, then max_features=sqrt(n_features).
  • If “sqrt”, then max_features=sqrt(n_features).
  • If “log2”, then max_features=log2(n_features).
  • If None, then max_features=n_features.

Note: the search for a split does not stop until at least one valid partition of the node samples is found, even if it requires to effectively inspect more than max_features features.

max_leaf_nodes : int or None, optional (default=None)
Grow trees with max_leaf_nodes in best-first fashion. Best nodes are defined as relative reduction in impurity. If None then unlimited number of leaf nodes.
min_impurity_decrease : float, optional (default=0.)

A node will be split if this split induces a decrease of the impurity greater than or equal to this value.

The weighted impurity decrease equation is the following:

N_t / N * (impurity - N_t_R / N_t * right_impurity
                    - N_t_L / N_t * left_impurity)

where N is the total number of samples, N_t is the number of samples at the current node, N_t_L is the number of samples in the left child, and N_t_R is the number of samples in the right child.

N, N_t, N_t_R and N_t_L all refer to the weighted sum, if sample_weight is passed.

New in version 0.19.

min_impurity_split : float, (default=1e-7)

Threshold for early stopping in tree growth. A node will split if its impurity is above the threshold, otherwise it is a leaf.

Deprecated since version 0.19: min_impurity_split has been deprecated in favor of min_impurity_decrease in 0.19. The default value of min_impurity_split will change from 1e-7 to 0 in 0.23 and it will be removed in 0.25. Use min_impurity_decrease instead.

bootstrap : boolean, optional (default=False)
Whether bootstrap samples are used when building trees. If False, the whole datset is used to build each tree.
oob_score : bool, optional (default=False)
Whether to use out-of-bag samples to estimate the generalization accuracy.
n_jobs : int or None, optional (default=None)
The number of jobs to run in parallel for both fit and predict. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
random_state : int, RandomState instance or None, optional (default=None)
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.
verbose : int, optional (default=0)
Controls the verbosity when fitting and predicting.
warm_start : bool, optional (default=False)
When set to True, reuse the solution of the previous call to fit and add more estimators to the ensemble, otherwise, just fit a whole new forest. See the Glossary.
class_weight : dict, list of dicts, “balanced”, “balanced_subsample” or None, optional (default=None)

Weights associated with classes in the form {class_label: weight}. If not given, all classes are supposed to have weight one. For multi-output problems, a list of dicts can be provided in the same order as the columns of y.

Note that for multioutput (including multilabel) weights should be defined for each class of every column in its own dict. For example, for four-class multilabel classification weights should be [{0: 1, 1: 1}, {0: 1, 1: 5}, {0: 1, 1: 1}, {0: 1, 1: 1}] instead of [{1:1}, {2:5}, {3:1}, {4:1}].

The “balanced” mode uses the values of y to automatically adjust weights inversely proportional to class frequencies in the input data as n_samples / (n_classes * np.bincount(y))

The “balanced_subsample” mode is the same as “balanced” except that weights are computed based on the bootstrap sample for every tree grown.

For multi-output, the weights of each column of y will be multiplied.

Note that these weights will be multiplied with sample_weight (passed through the fit method) if sample_weight is specified.

Attributes

estimators_ : list of DecisionTreeClassifier
The collection of fitted sub-estimators.
classes_ : array of shape = [n_classes] or a list of such arrays
The classes labels (single output problem), or a list of arrays of class labels (multi-output problem).
n_classes_ : int or list
The number of classes (single output problem), or a list containing the number of classes for each output (multi-output problem).
feature_importances_ : array of shape = [n_features]
The feature importances (the higher, the more important the feature).
n_features_ : int
The number of features when fit is performed.
n_outputs_ : int
The number of outputs when fit is performed.
oob_score_ : float
Score of the training dataset obtained using an out-of-bag estimate.
oob_decision_function_ : array of shape = [n_samples, n_classes]
Decision function computed with out-of-bag estimate on the training set. If n_estimators is small it might be possible that a data point was never left out during the bootstrap. In this case, oob_decision_function_ might contain NaN.

Notes

The default values for the parameters controlling the size of the trees (e.g. max_depth, min_samples_leaf, etc.) lead to fully grown and unpruned trees which can potentially be very large on some data sets. To reduce memory consumption, the complexity and size of the trees should be controlled by setting those parameter values.

References

[1]P. Geurts, D. Ernst., and L. Wehenkel, “Extremely randomized trees”, Machine Learning, 63(1), 3-42, 2006.

See also

sklearn.tree.ExtraTreeClassifier : Base classifier for this ensemble. RandomForestClassifier : Ensemble Classifier based on trees with optimal

splits.

Full API documentation: ExtraTreesClassifierScikitsLearnNode

class mdp.nodes.GridSearchCVScikitsLearnNode

Exhaustive search over specified parameter values for an estimator. This node has been automatically generated by wrapping the sklearn.model_selection._search.GridSearchCV class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Important members are fit, predict.

GridSearchCV implements a “fit” and a “score” method. It also implements “predict”, “predict_proba”, “decision_function”, “transform” and “inverse_transform” if they are implemented in the estimator used.

The parameters of the estimator used to apply these methods are optimized by cross-validated grid-search over a parameter grid.

Read more in the User Guide.

Parameters

estimator : estimator object.
This is assumed to implement the scikit-learn estimator interface. Either estimator needs to provide a score function, or scoring must be passed.
param_grid : dict or list of dictionaries
Dictionary with parameters names (string) as keys and lists of parameter settings to try as values, or a list of such dictionaries, in which case the grids spanned by each dictionary in the list are explored. This enables searching over any sequence of parameter settings.
scoring : string, callable, list/tuple, dict or None, default: None

A single string (see scoring_parameter) or a callable (see scoring) to evaluate the predictions on the test set.

For evaluating multiple metrics, either give a list of (unique) strings or a dict with names as keys and callables as values.

NOTE that when using custom scorers, each scorer should return a single value. Metric functions returning a list/array of values can be wrapped into multiple scorers that return one value each.

See multimetric_grid_search for an example.

If None, the estimator’s default scorer (if available) is used.

fit_params : dict, optional

Parameters to pass to the fit method.

Deprecated since version 0.19: fit_params as a constructor argument was deprecated in version 0.19 and will be removed in version 0.21. Pass fit parameters to the fit method instead.

n_jobs : int or None, optional (default=None)
Number of jobs to run in parallel. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
pre_dispatch : int, or string, optional

Controls the number of jobs that get dispatched during parallel execution. Reducing this number can be useful to avoid an explosion of memory consumption when more jobs get dispatched than CPUs can process. This parameter can be:

  • None, in which case all the jobs are immediately created and spawned. Use this for lightweight and fast-running jobs, to avoid delays due to on-demand spawning of the jobs
  • An int, giving the exact number of total jobs that are spawned
  • A string, giving an expression as a function of n_jobs, as in ‘2*n_jobs’
iid : boolean, default=’warn’

If True, return the average score across folds, weighted by the number of samples in each test set. In this case, the data is assumed to be identically distributed across the folds, and the loss minimized is the total loss per sample, and not the mean loss across the folds. If False, return the average score across folds. Default is True, but will change to False in version 0.21, to correspond to the standard definition of cross-validation.

Changed in version 0.20: Parameter iid will change from True to False by default in version 0.22, and will be removed in 0.24.

cv : int, cross-validation generator or an iterable, optional

Determines the cross-validation splitting strategy. Possible inputs for cv are:

  • None, to use the default 3-fold cross validation,
  • integer, to specify the number of folds in a (Stratified)KFold,
  • CV splitter,
  • An iterable yielding (train, test) splits as arrays of indices.

For integer/None inputs, if the estimator is a classifier and y is either binary or multiclass, StratifiedKFold is used. In all other cases, KFold is used.

Refer User Guide for the various cross-validation strategies that can be used here.

Changed in version 0.20: cv default value if None will change from 3-fold to 5-fold in v0.22.

refit : boolean, or string, default=True

Refit an estimator using the best found parameters on the whole dataset.

For multiple metric evaluation, this needs to be a string denoting the scorer is used to find the best parameters for refitting the estimator at the end.

The refitted estimator is made available at the best_estimator_ attribute and permits using predict directly on this GridSearchCV instance.

Also for multiple metric evaluation, the attributes best_index_, best_score_ and best_params_ will only be available if refit is set and all of them will be determined w.r.t this specific scorer.

See scoring parameter to know more about multiple metric evaluation.

verbose : integer
Controls the verbosity: the higher, the more messages.
error_score : ‘raise’ or numeric
Value to assign to the score if an error occurs in estimator fitting. If set to ‘raise’, the error is raised. If a numeric value is given, FitFailedWarning is raised. This parameter does not affect the refit step, which will always raise the error. Default is ‘raise’ but from version 0.22 it will change to np.nan.
return_train_score : boolean, optional

If False, the cv_results_ attribute will not include training scores.

Current default is 'warn', which behaves as True in addition to raising a warning when a training score is looked up. That default will be changed to False in 0.21. Computing training scores is used to get insights on how different parameter settings impact the overfitting/underfitting trade-off. However computing the scores on the training set can be computationally expensive and is not strictly required to select the parameters that yield the best generalization performance.

Examples

>>> from sklearn import svm, datasets
>>> from sklearn.model_selection import GridSearchCV
>>> iris = datasets.load_iris()
>>> parameters = {'kernel':('linear', 'rbf'), 'C':[1, 10]}
>>> svc = svm.SVC(gamma="scale")
>>> clf = GridSearchCV(svc, parameters, cv=5)
>>> clf.fit(iris.data, iris.target)
...                             
GridSearchCV(cv=5, error_score=...,
       estimator=SVC(C=1.0, cache_size=..., class_weight=..., coef0=...,
                     decision_function_shape='ovr', degree=..., gamma=...,
                     kernel='rbf', max_iter=-1, probability=False,
                     random_state=None, shrinking=True, tol=...,
                     verbose=False),
       fit_params=None, iid=..., n_jobs=None,
       param_grid=..., pre_dispatch=..., refit=..., return_train_score=...,
       scoring=..., verbose=...)
>>> sorted(clf.cv_results_.keys())
...                             
['mean_fit_time', 'mean_score_time', 'mean_test_score',...
 'mean_train_score', 'param_C', 'param_kernel', 'params',...
 'rank_test_score', 'split0_test_score',...
 'split0_train_score', 'split1_test_score', 'split1_train_score',...
 'split2_test_score', 'split2_train_score',...
 'std_fit_time', 'std_score_time', 'std_test_score', 'std_train_score'...]

Attributes

cv_results_ : dict of numpy (masked) ndarrays

A dict with keys as column headers and values as columns, that can be imported into a pandas DataFrame.

For instance the below given table

param_kernel param_gamma param_degree split0_test_score rank_t…
‘poly’ 2 0.80 2
‘poly’ 3 0.70 4
‘rbf’ 0.1 0.80 3
‘rbf’ 0.2 0.93 1

will be represented by a cv_results_ dict of:

{
'param_kernel': masked_array(data = ['poly', 'poly', 'rbf', 'rbf'],
                             mask = [False False False False]...)
'param_gamma': masked_array(data = [-- -- 0.1 0.2],
                            mask = [ True  True False False]...),
'param_degree': masked_array(data = [2.0 3.0 -- --],
                             mask = [False False  True  True]...),
'split0_test_score'  : [0.80, 0.70, 0.80, 0.93],
'split1_test_score'  : [0.82, 0.50, 0.70, 0.78],
'mean_test_score'    : [0.81, 0.60, 0.75, 0.85],
'std_test_score'     : [0.01, 0.10, 0.05, 0.08],
'rank_test_score'    : [2, 4, 3, 1],
'split0_train_score' : [0.80, 0.92, 0.70, 0.93],
'split1_train_score' : [0.82, 0.55, 0.70, 0.87],
'mean_train_score'   : [0.81, 0.74, 0.70, 0.90],
'std_train_score'    : [0.01, 0.19, 0.00, 0.03],
'mean_fit_time'      : [0.73, 0.63, 0.43, 0.49],
'std_fit_time'       : [0.01, 0.02, 0.01, 0.01],
'mean_score_time'    : [0.01, 0.06, 0.04, 0.04],
'std_score_time'     : [0.00, 0.00, 0.00, 0.01],
'params'             : [{'kernel': 'poly', 'degree': 2}, ...],
}

NOTE

The key 'params' is used to store a list of parameter settings dicts for all the parameter candidates.

The mean_fit_time, std_fit_time, mean_score_time and std_score_time are all in seconds.

For multi-metric evaluation, the scores for all the scorers are available in the cv_results_ dict at the keys ending with that scorer’s name ('_<scorer_name>') instead of '_score' shown above. (‘split0_test_precision’, ‘mean_train_precision’ etc.)

best_estimator_ : estimator or dict

Estimator that was chosen by the search, i.e. estimator which gave highest score (or smallest loss if specified) on the left out data. Not available if refit=False.

See refit parameter for more information on allowed values.

best_score_ : float

Mean cross-validated score of the best_estimator

For multi-metric evaluation, this is present only if refit is specified.

best_params_ : dict

Parameter setting that gave the best results on the hold out data.

For multi-metric evaluation, this is present only if refit is specified.

best_index_ : int

The index (of the cv_results_ arrays) which corresponds to the best candidate parameter setting.

The dict at search.cv_results_['params'][search.best_index_] gives the parameter setting for the best model, that gives the highest mean score (search.best_score_).

For multi-metric evaluation, this is present only if refit is specified.

scorer_ : function or a dict

Scorer function used on the held out data to choose the best parameters for the model.

For multi-metric evaluation, this attribute holds the validated scoring dict which maps the scorer key to the scorer callable.

n_splits_ : int
The number of cross-validation splits (folds/iterations).
refit_time_ : float

Seconds used for refitting the best model on the whole dataset.

This is present only if refit is not False.

Notes

The parameters selected are those that maximize the score of the left out data, unless an explicit score is passed in which case it is used instead.

If n_jobs was set to a value higher than one, the data is copied for each point in the grid (and not n_jobs times). This is done for efficiency reasons if individual jobs take very little time, but may raise errors if the dataset is large and not enough memory is available. A workaround in this case is to set pre_dispatch. Then, the memory is copied only pre_dispatch many times. A reasonable value for pre_dispatch is 2 * n_jobs.

See Also

ParameterGrid:

  • generates all the combinations of a hyperparameter grid.

sklearn.model_selection.train_test_split():

  • utility function to split the data into a development set usable
  • for fitting a GridSearchCV instance and an evaluation set for
  • its final evaluation.

sklearn.metrics.make_scorer():

  • Make a scorer from a performance metric or loss function.

Full API documentation: GridSearchCVScikitsLearnNode

class mdp.nodes.LassoCVScikitsLearnNode

Lasso linear model with iterative fitting along a regularization path. This node has been automatically generated by wrapping the sklearn.linear_model.coordinate_descent.LassoCV class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. See glossary entry for cross-validation estimator.

The best model is selected by cross-validation.

The optimization objective for Lasso is:

(1 / (2 * n_samples)) * ||y - Xw||^2_2 + alpha * ||w||_1

Read more in the User Guide.

Parameters

eps : float, optional
Length of the path. eps=1e-3 means that alpha_min / alpha_max = 1e-3.
n_alphas : int, optional
Number of alphas along the regularization path
alphas : numpy array, optional
List of alphas where to compute the models. If None alphas are set automatically
fit_intercept : boolean, default True
whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (e.g. data is expected to be already centered).
normalize : boolean, optional, default False
This parameter is ignored when fit_intercept is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use sklearn.preprocessing.StandardScaler before calling fit on an estimator with normalize=False.
precompute : True | False | ‘auto’ | array-like
Whether to use a precomputed Gram matrix to speed up calculations. If set to 'auto' let us decide. The Gram matrix can also be passed as argument.
max_iter : int, optional
The maximum number of iterations
tol : float, optional
The tolerance for the optimization: if the updates are smaller than tol, the optimization code checks the dual gap for optimality and continues until it is smaller than tol.
copy_X : boolean, optional, default True
If True, X will be copied; else, it may be overwritten.
cv : int, cross-validation generator or an iterable, optional

Determines the cross-validation splitting strategy. Possible inputs for cv are:

  • None, to use the default 3-fold cross-validation,
  • integer, to specify the number of folds.
  • CV splitter,
  • An iterable yielding (train, test) splits as arrays of indices.

For integer/None inputs, KFold is used.

Refer User Guide for the various cross-validation strategies that can be used here.

Changed in version 0.20: cv default value if None will change from 3-fold to 5-fold in v0.22.

verbose : bool or integer
Amount of verbosity.
n_jobs : int or None, optional (default=None)
Number of CPUs to use during the cross validation. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
positive : bool, optional
If positive, restrict regression coefficients to be positive
random_state : int, RandomState instance or None, optional, default None
The seed of the pseudo random number generator that selects a random feature to update. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random. Used when selection == ‘random’.
selection : str, default ‘cyclic’
If set to ‘random’, a random coefficient is updated every iteration rather than looping over features sequentially by default. This (setting to ‘random’) often leads to significantly faster convergence especially when tol is higher than 1e-4.

Attributes

alpha_ : float
The amount of penalization chosen by cross validation
coef_ : array, shape (n_features,) | (n_targets, n_features)
parameter vector (w in the cost function formula)
intercept_ : float | array, shape (n_targets,)
independent term in decision function.
mse_path_ : array, shape (n_alphas, n_folds)
mean square error for the test set on each fold, varying alpha
alphas_ : numpy array, shape (n_alphas,)
The grid of alphas used for fitting
dual_gap_ : ndarray, shape ()
The dual gap at the end of the optimization for the optimal alpha (alpha_).
n_iter_ : int
number of iterations run by the coordinate descent solver to reach the specified tolerance for the optimal alpha.

Examples

>>> from sklearn.linear_model import LassoCV
>>> from sklearn.datasets import make_regression
>>> X, y = make_regression(noise=4, random_state=0)
>>> reg = LassoCV(cv=5, random_state=0).fit(X, y)
>>> reg.score(X, y) 
0.9993...
>>> reg.predict(X[:1,])
array([-78.4951...])

Notes

For an example, see examples/linear_model/plot_lasso_model_selection.py.

To avoid unnecessary memory duplication the X argument of the fit method should be directly passed as a Fortran-contiguous numpy array.

See also

lars_path lasso_path LassoLars Lasso LassoLarsCV

Full API documentation: LassoCVScikitsLearnNode

class mdp.nodes.OneClassSVMScikitsLearnNode

Unsupervised Outlier Detection. This node has been automatically generated by wrapping the sklearn.svm.classes.OneClassSVM class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Estimate the support of a high-dimensional distribution.

The implementation is based on libsvm.

Read more in the User Guide.

Parameters

kernel : string, optional (default=’rbf’)
Specifies the kernel type to be used in the algorithm. It must be one of ‘linear’, ‘poly’, ‘rbf’, ‘sigmoid’, ‘precomputed’ or a callable. If none is given, ‘rbf’ will be used. If a callable is given it is used to precompute the kernel matrix.
degree : int, optional (default=3)
Degree of the polynomial kernel function (‘poly’). Ignored by all other kernels.
gamma : float, optional (default=’auto’)

Kernel coefficient for ‘rbf’, ‘poly’ and ‘sigmoid’.

Current default is ‘auto’ which uses 1 / n_features, if gamma='scale' is passed then it uses 1 / (n_features * X.var()) as value of gamma. The current default of gamma, ‘auto’, will change to ‘scale’ in version 0.22. ‘auto_deprecated’, a deprecated version of ‘auto’ is used as a default indicating that no explicit value of gamma was passed.

coef0 : float, optional (default=0.0)
Independent term in kernel function. It is only significant in ‘poly’ and ‘sigmoid’.
tol : float, optional
Tolerance for stopping criterion.
nu : float, optional
An upper bound on the fraction of training errors and a lower bound of the fraction of support vectors. Should be in the interval (0, 1]. By default 0.5 will be taken.
shrinking : boolean, optional
Whether to use the shrinking heuristic.
cache_size : float, optional
Specify the size of the kernel cache (in MB).
verbose : bool, default: False
Enable verbose output. Note that this setting takes advantage of a per-process runtime setting in libsvm that, if enabled, may not work properly in a multithreaded context.
max_iter : int, optional (default=-1)
Hard limit on iterations within solver, or -1 for no limit.
random_state : int, RandomState instance or None, optional (default=None)

Ignored.

Deprecated since version 0.20: random_state has been deprecated in 0.20 and will be removed in 0.22.

Attributes

support_ : array-like, shape = [n_SV]
Indices of support vectors.
support_vectors_ : array-like, shape = [nSV, n_features]
Support vectors.
dual_coef_ : array, shape = [1, n_SV]
Coefficients of the support vectors in the decision function.
coef_ : array, shape = [1, n_features]

Weights assigned to the features (coefficients in the primal problem). This is only available in the case of a linear kernel.

coef_ is readonly property derived from dual_coef_ and support_vectors_

intercept_ : array, shape = [1,]
Constant in the decision function.
offset_ : float
Offset used to define the decision function from the raw scores. We have the relation: decision_function = score_samples - offset_. The offset is the opposite of intercept_ and is provided for consistency with other outlier detection algorithms.

Full API documentation: OneClassSVMScikitsLearnNode

class mdp.nodes.RidgeCVScikitsLearnNode

Ridge regression with built-in cross-validation. This node has been automatically generated by wrapping the sklearn.linear_model.ridge.RidgeCV class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. See glossary entry for cross-validation estimator.

By default, it performs Generalized Cross-Validation, which is a form of efficient Leave-One-Out cross-validation.

Read more in the User Guide.

Parameters

alphas : numpy array of shape [n_alphas]
Array of alpha values to try. Regularization strength; must be a positive float. Regularization improves the conditioning of the problem and reduces the variance of the estimates. Larger values specify stronger regularization. Alpha corresponds to C^-1 in other linear models such as LogisticRegression or LinearSVC.
fit_intercept : boolean
Whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (e.g. data is expected to be already centered).
normalize : boolean, optional, default False
This parameter is ignored when fit_intercept is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use sklearn.preprocessing.StandardScaler before calling fit on an estimator with normalize=False.
scoring : string, callable or None, optional, default: None
A string (see model evaluation documentation) or a scorer callable object / function with signature scorer(estimator, X, y).
cv : int, cross-validation generator or an iterable, optional

Determines the cross-validation splitting strategy. Possible inputs for cv are:

  • None, to use the efficient Leave-One-Out cross-validation
  • integer, to specify the number of folds.
  • CV splitter,
  • An iterable yielding (train, test) splits as arrays of indices.

For integer/None inputs, if y is binary or multiclass, sklearn.model_selection.StratifiedKFold is used, else, sklearn.model_selection.KFold is used.

Refer User Guide for the various cross-validation strategies that can be used here.

gcv_mode : {None, ‘auto’, ‘svd’, eigen’}, optional

Flag indicating which strategy to use when performing Generalized Cross-Validation. Options are:

'auto' : use svd if n_samples > n_features or when X is a sparse
         matrix, otherwise use eigen
'svd' : force computation via singular value decomposition of X
        (does not work for sparse matrices)
'eigen' : force computation via eigendecomposition of X^T X

The ‘auto’ mode is the default and is intended to pick the cheaper option of the two depending upon the shape and format of the training data.

store_cv_values : boolean, default=False
Flag indicating if the cross-validation values corresponding to each alpha should be stored in the cv_values_ attribute (see below). This flag is only compatible with cv=None (i.e. using Generalized Cross-Validation).

Attributes

cv_values_ : array, shape = [n_samples, n_alphas] or shape = [n_samples, n_targets, n_alphas], optional
Cross-validation values for each alpha (if store_cv_values=True and cv=None). After fit() has been called, this attribute will contain the mean squared errors (by default) or the values of the {loss,score}_func function (if provided in the constructor).
coef_ : array, shape = [n_features] or [n_targets, n_features]
Weight vector(s).
intercept_ : float | array, shape = (n_targets,)
Independent term in decision function. Set to 0.0 if fit_intercept = False.
alpha_ : float
Estimated regularization parameter.

Examples

>>> from sklearn.datasets import load_diabetes
>>> from sklearn.linear_model import RidgeCV
>>> X, y = load_diabetes(return_X_y=True)
>>> clf = RidgeCV(alphas=[1e-3, 1e-2, 1e-1, 1]).fit(X, y)
>>> clf.score(X, y) 
0.5166...

See also

Ridge : Ridge regression RidgeClassifier : Ridge classifier RidgeClassifierCV : Ridge classifier with built-in cross validation

Full API documentation: RidgeCVScikitsLearnNode

class mdp.nodes.LinearDiscriminantAnalysisScikitsLearnNode

Linear Discriminant Analysis This node has been automatically generated by wrapping the sklearn.discriminant_analysis.LinearDiscriminantAnalysis class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. A classifier with a linear decision boundary, generated by fitting class conditional densities to the data and using Bayes’ rule.

The model fits a Gaussian density to each class, assuming that all classes share the same covariance matrix.

The fitted model can also be used to reduce the dimensionality of the input by projecting it to the most discriminative directions.

New in version 0.17: LinearDiscriminantAnalysis.

Read more in the User Guide.

Parameters

solver : string, optional

Solver to use, possible values:

    • ‘svd’: Singular value decomposition (default).
  • Does not compute the covariance matrix, therefore this solver is
  • recommended for data with a large number of features.
    • ‘lsqr’: Least squares solution, can be combined with shrinkage.
    • ‘eigen’: Eigenvalue decomposition, can be combined with shrinkage.
shrinkage : string or float, optional

Shrinkage parameter, possible values:

    • None: no shrinkage (default).
    • ‘auto’: automatic shrinkage using the Ledoit-Wolf lemma.
    • float between 0 and 1: fixed shrinkage parameter.

Note that shrinkage works only with ‘lsqr’ and ‘eigen’ solvers.

priors : array, optional, shape (n_classes,)
Class priors.
n_components : int, optional
Number of components (< n_classes - 1) for dimensionality reduction.
store_covariance : bool, optional

Additionally compute class covariance matrix (default False), used only in ‘svd’ solver.

New in version 0.17.

tol : float, optional, (default 1.0e-4)

Threshold used for rank estimation in SVD solver.

New in version 0.17.

Attributes

coef_ : array, shape (n_features,) or (n_classes, n_features)
Weight vector(s).
intercept_ : array, shape (n_features,)
Intercept term.
covariance_ : array-like, shape (n_features, n_features)
Covariance matrix (shared by all classes).
explained_variance_ratio_ : array, shape (n_components,)
Percentage of variance explained by each of the selected components. If n_components is not set then all components are stored and the sum of explained variances is equal to 1.0. Only available when eigen or svd solver is used.
means_ : array-like, shape (n_classes, n_features)
Class means.
priors_ : array-like, shape (n_classes,)
Class priors (sum to 1).
scalings_ : array-like, shape (rank, n_classes - 1)
Scaling of the features in the space spanned by the class centroids.
xbar_ : array-like, shape (n_features,)
Overall mean.
classes_ : array-like, shape (n_classes,)
Unique class labels.

See also

sklearn.discriminant_analysis.QuadraticDiscriminantAnalysis: Quadratic
Discriminant Analysis

Notes

The default solver is ‘svd’. It can perform both classification and transform, and it does not rely on the calculation of the covariance matrix. This can be an advantage in situations where the number of features is large. However, the ‘svd’ solver cannot be used with shrinkage.

The ‘lsqr’ solver is an efficient algorithm that only works for classification. It supports shrinkage.

The ‘eigen’ solver is based on the optimization of the between class scatter to within class scatter ratio. It can be used for both classification and transform, and it supports shrinkage. However, the ‘eigen’ solver needs to compute the covariance matrix, so it might not be suitable for situations with a high number of features.

Examples

>>> import numpy as np
>>> from sklearn.discriminant_analysis import LinearDiscriminantAnalysis
>>> X = np.array([[-1, -1], [-2, -1], [-3, -2], [1, 1], [2, 1], [3, 2]])
>>> y = np.array([1, 1, 1, 2, 2, 2])
>>> clf = LinearDiscriminantAnalysis()
>>> clf.fit(X, y)
LinearDiscriminantAnalysis(n_components=None, priors=None, shrinkage=None,
              solver='svd', store_covariance=False, tol=0.0001)
>>> print(clf.predict([[-0.8, -1]]))
[1]

Full API documentation: LinearDiscriminantAnalysisScikitsLearnNode

class mdp.nodes.PriorProbabilityEstimatorScikitsLearnNode

An estimator predicting the probability of each This node has been automatically generated by wrapping the sklearn.ensemble.gradient_boosting.PriorProbabilityEstimator class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute.

Full API documentation: PriorProbabilityEstimatorScikitsLearnNode

class mdp.nodes.ARDRegressionScikitsLearnNode

Bayesian ARD regression. This node has been automatically generated by wrapping the sklearn.linear_model.bayes.ARDRegression class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Fit the weights of a regression model, using an ARD prior. The weights of the regression model are assumed to be in Gaussian distributions. Also estimate the parameters lambda (precisions of the distributions of the weights) and alpha (precision of the distribution of the noise). The estimation is done by an iterative procedures (Evidence Maximization)

Read more in the User Guide.

Parameters

n_iter : int, optional
Maximum number of iterations. Default is 300
tol : float, optional
Stop the algorithm if w has converged. Default is 1.e-3.
alpha_1 : float, optional
Hyper-parameter : shape parameter for the Gamma distribution prior over the alpha parameter. Default is 1.e-6.
alpha_2 : float, optional
Hyper-parameter : inverse scale parameter (rate parameter) for the Gamma distribution prior over the alpha parameter. Default is 1.e-6.
lambda_1 : float, optional
Hyper-parameter : shape parameter for the Gamma distribution prior over the lambda parameter. Default is 1.e-6.
lambda_2 : float, optional
Hyper-parameter : inverse scale parameter (rate parameter) for the Gamma distribution prior over the lambda parameter. Default is 1.e-6.
compute_score : boolean, optional
If True, compute the objective function at each step of the model. Default is False.
threshold_lambda : float, optional
threshold for removing (pruning) weights with high precision from the computation. Default is 1.e+4.
fit_intercept : boolean, optional
whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (e.g. data is expected to be already centered). Default is True.
normalize : boolean, optional, default False
This parameter is ignored when fit_intercept is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use sklearn.preprocessing.StandardScaler before calling fit on an estimator with normalize=False.
copy_X : boolean, optional, default True.
If True, X will be copied; else, it may be overwritten.
verbose : boolean, optional, default False
Verbose mode when fitting the model.

Attributes

coef_ : array, shape = (n_features)
Coefficients of the regression model (mean of distribution)
alpha_ : float
estimated precision of the noise.
lambda_ : array, shape = (n_features)
estimated precisions of the weights.
sigma_ : array, shape = (n_features, n_features)
estimated variance-covariance matrix of the weights
scores_ : float
if computed, value of the objective function (to be maximized)

Examples

>>> from sklearn import linear_model
>>> clf = linear_model.ARDRegression()
>>> clf.fit([[0,0], [1, 1], [2, 2]], [0, 1, 2])
... 
ARDRegression(alpha_1=1e-06, alpha_2=1e-06, compute_score=False,
        copy_X=True, fit_intercept=True, lambda_1=1e-06, lambda_2=1e-06,
        n_iter=300, normalize=False, threshold_lambda=10000.0, tol=0.001,
        verbose=False)
>>> clf.predict([[1, 1]])
array([1.])

Notes

For an example, see examples/linear_model/plot_ard.py.

References

D. J. C. MacKay, Bayesian nonlinear modeling for the prediction competition, ASHRAE Transactions, 1994.

R. Salakhutdinov, Lecture notes on Statistical Machine Learning, http://www.utstat.toronto.edu/~rsalakhu/sta4273/notes/Lecture2.pdf#page=15 Their beta is our self.alpha_ Their alpha is our self.lambda_ ARD is a little different than the slide: only dimensions/features for which self.lambda_ < self.threshold_lambda are kept and the rest are discarded.

Full API documentation: ARDRegressionScikitsLearnNode

class mdp.nodes.ImputerScikitsLearnNode

Imputation transformer for completing missing values. This node has been automatically generated by wrapping the sklearn.preprocessing.imputation.Imputer class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Read more in the User Guide.

Parameters

missing_values : integer or “NaN”, optional (default=”NaN”)
The placeholder for the missing values. All occurrences of missing_values will be imputed. For missing values encoded as np.nan, use the string value “NaN”.
strategy : string, optional (default=”mean”)

The imputation strategy.

  • If “mean”, then replace missing values using the mean along the axis.
  • If “median”, then replace missing values using the median along the axis.
  • If “most_frequent”, then replace missing using the most frequent value along the axis.
axis : integer, optional (default=0)

The axis along which to impute.

  • If axis=0, then impute along columns.
  • If axis=1, then impute along rows.
verbose : integer, optional (default=0)
Controls the verbosity of the imputer.
copy : boolean, optional (default=True)

If True, a copy of X will be created. If False, imputation will be done in-place whenever possible. Note that, in the following cases, a new copy will always be made, even if copy=False:

  • If X is not an array of floating values;
  • If X is sparse and missing_values=0;
  • If axis=0 and X is encoded as a CSR matrix;
  • If axis=1 and X is encoded as a CSC matrix.

Attributes

statistics_ : array of shape (n_features,)
The imputation fill value for each feature if axis == 0.

Notes

  • When axis=0, columns which only contained missing values at fit are discarded upon transform.
  • When axis=1, an exception is raised if there are rows for which it is not possible to fill in the missing values (e.g., because they only contain missing values).

Full API documentation: ImputerScikitsLearnNode

class mdp.nodes.VarianceThresholdScikitsLearnNode

Feature selector that removes all low-variance features. This node has been automatically generated by wrapping the sklearn.feature_selection.variance_threshold.VarianceThreshold class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. This feature selection algorithm looks only at the features (X), not the desired outputs (y), and can thus be used for unsupervised learning.

Read more in the User Guide.

Parameters

threshold : float, optional
Features with a training-set variance lower than this threshold will be removed. The default is to keep all features with non-zero variance, i.e. remove the features that have the same value in all samples.

Attributes

variances_ : array, shape (n_features,)
Variances of individual features.

Examples

The following dataset has integer features, two of which are the same in every sample. These are removed with the default setting for threshold:

>>> X = [[0, 2, 0, 3], [0, 1, 4, 3], [0, 1, 1, 3]]
>>> selector = VarianceThreshold()
>>> selector.fit_transform(X)
array([[2, 0],
       [1, 4],
       [1, 1]])

Full API documentation: VarianceThresholdScikitsLearnNode

class mdp.nodes.GradientBoostingRegressorScikitsLearnNode

Gradient Boosting for regression. This node has been automatically generated by wrapping the sklearn.ensemble.gradient_boosting.GradientBoostingRegressor class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. GB builds an additive model in a forward stage-wise fashion; it allows for the optimization of arbitrary differentiable loss functions. In each stage a regression tree is fit on the negative gradient of the given loss function.

Read more in the User Guide.

Parameters

loss : {‘ls’, ‘lad’, ‘huber’, ‘quantile’}, optional (default=’ls’)
loss function to be optimized. ‘ls’ refers to least squares regression. ‘lad’ (least absolute deviation) is a highly robust loss function solely based on order information of the input variables. ‘huber’ is a combination of the two. ‘quantile’ allows quantile regression (use alpha to specify the quantile).
learning_rate : float, optional (default=0.1)
learning rate shrinks the contribution of each tree by learning_rate. There is a trade-off between learning_rate and n_estimators.
n_estimators : int (default=100)
The number of boosting stages to perform. Gradient boosting is fairly robust to over-fitting so a large number usually results in better performance.
subsample : float, optional (default=1.0)
The fraction of samples to be used for fitting the individual base learners. If smaller than 1.0 this results in Stochastic Gradient Boosting. subsample interacts with the parameter n_estimators. Choosing subsample < 1.0 leads to a reduction of variance and an increase in bias.
criterion : string, optional (default=”friedman_mse”)

The function to measure the quality of a split. Supported criteria are “friedman_mse” for the mean squared error with improvement score by Friedman, “mse” for mean squared error, and “mae” for the mean absolute error. The default value of “friedman_mse” is generally the best as it can provide a better approximation in some cases.

New in version 0.18.

min_samples_split : int, float, optional (default=2)

The minimum number of samples required to split an internal node:

  • If int, then consider min_samples_split as the minimum number.
  • If float, then min_samples_split is a fraction and ceil(min_samples_split * n_samples) are the minimum number of samples for each split.

Changed in version 0.18: Added float values for fractions.

min_samples_leaf : int, float, optional (default=1)

The minimum number of samples required to be at a leaf node. A split point at any depth will only be considered if it leaves at least min_samples_leaf training samples in each of the left and right branches. This may have the effect of smoothing the model, especially in regression.

  • If int, then consider min_samples_leaf as the minimum number.
  • If float, then min_samples_leaf is a fraction and ceil(min_samples_leaf * n_samples) are the minimum number of samples for each node.

Changed in version 0.18: Added float values for fractions.

min_weight_fraction_leaf : float, optional (default=0.)
The minimum weighted fraction of the sum total of weights (of all the input samples) required to be at a leaf node. Samples have equal weight when sample_weight is not provided.
max_depth : integer, optional (default=3)
maximum depth of the individual regression estimators. The maximum depth limits the number of nodes in the tree. Tune this parameter for best performance; the best value depends on the interaction of the input variables.
min_impurity_decrease : float, optional (default=0.)

A node will be split if this split induces a decrease of the impurity greater than or equal to this value.

The weighted impurity decrease equation is the following:

N_t / N * (impurity - N_t_R / N_t * right_impurity
                    - N_t_L / N_t * left_impurity)

where N is the total number of samples, N_t is the number of samples at the current node, N_t_L is the number of samples in the left child, and N_t_R is the number of samples in the right child.

N, N_t, N_t_R and N_t_L all refer to the weighted sum, if sample_weight is passed.

New in version 0.19.

min_impurity_split : float, (default=1e-7)

Threshold for early stopping in tree growth. A node will split if its impurity is above the threshold, otherwise it is a leaf.

Deprecated since version 0.19: min_impurity_split has been deprecated in favor of min_impurity_decrease in 0.19. The default value of min_impurity_split will change from 1e-7 to 0 in 0.23 and it will be removed in 0.25. Use min_impurity_decrease instead.

init : estimator, optional (default=None)
An estimator object that is used to compute the initial predictions. init has to provide fit and predict. If None it uses loss.init_estimator.
random_state : int, RandomState instance or None, optional (default=None)
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.
max_features : int, float, string or None, optional (default=None)

The number of features to consider when looking for the best split:

  • If int, then consider max_features features at each split.
  • If float, then max_features is a fraction and int(max_features * n_features) features are considered at each split.
  • If “auto”, then max_features=n_features.
  • If “sqrt”, then max_features=sqrt(n_features).
  • If “log2”, then max_features=log2(n_features).
  • If None, then max_features=n_features.

Choosing max_features < n_features leads to a reduction of variance and an increase in bias.

Note: the search for a split does not stop until at least one valid partition of the node samples is found, even if it requires to effectively inspect more than max_features features.

alpha : float (default=0.9)
The alpha-quantile of the huber loss function and the quantile loss function. Only if loss='huber' or loss='quantile'.
verbose : int, default: 0
Enable verbose output. If 1 then it prints progress and performance once in a while (the more trees the lower the frequency). If greater than 1 then it prints progress and performance for every tree.
max_leaf_nodes : int or None, optional (default=None)
Grow trees with max_leaf_nodes in best-first fashion. Best nodes are defined as relative reduction in impurity. If None then unlimited number of leaf nodes.
warm_start : bool, default: False
When set to True, reuse the solution of the previous call to fit and add more estimators to the ensemble, otherwise, just erase the previous solution. See the Glossary.
presort : bool or ‘auto’, optional (default=’auto’)

Whether to presort the data to speed up the finding of best splits in fitting. Auto mode by default will use presorting on dense data and default to normal sorting on sparse data. Setting presort to true on sparse data will raise an error.

New in version 0.17: optional parameter presort.

validation_fraction : float, optional, default 0.1

The proportion of training data to set aside as validation set for early stopping. Must be between 0 and 1. Only used if n_iter_no_change is set to an integer.

New in version 0.20.

n_iter_no_change : int, default None

n_iter_no_change is used to decide if early stopping will be used to terminate training when validation score is not improving. By default it is set to None to disable early stopping. If set to a number, it will set aside validation_fraction size of the training data as validation and terminate training when validation score is not improving in all of the previous n_iter_no_change numbers of iterations.

New in version 0.20.

tol : float, optional, default 1e-4

Tolerance for the early stopping. When the loss is not improving by at least tol for n_iter_no_change iterations (if set to a number), the training stops.

New in version 0.20.

Attributes

feature_importances_ : array, shape (n_features,)
The feature importances (the higher, the more important the feature).
oob_improvement_ : array, shape (n_estimators,)
The improvement in loss (= deviance) on the out-of-bag samples relative to the previous iteration. oob_improvement_[0] is the improvement in loss of the first stage over the init estimator.
train_score_ : array, shape (n_estimators,)
The i-th score train_score_[i] is the deviance (= loss) of the model at iteration i on the in-bag sample. If subsample == 1 this is the deviance on the training data.
loss_ : LossFunction
The concrete LossFunction object.
init_ : estimator
The estimator that provides the initial predictions. Set via the init argument or loss.init_estimator.
estimators_ : array of DecisionTreeRegressor, shape (n_estimators, 1)
The collection of fitted sub-estimators.

Notes

The features are always randomly permuted at each split. Therefore, the best found split may vary, even with the same training data and max_features=n_features, if the improvement of the criterion is identical for several splits enumerated during the search of the best split. To obtain a deterministic behaviour during fitting, random_state has to be fixed.

See also

DecisionTreeRegressor, RandomForestRegressor

References

J. Friedman, Greedy Function Approximation: A Gradient Boosting Machine, The Annals of Statistics, Vol. 29, No. 5, 2001.

  1. Friedman, Stochastic Gradient Boosting, 1999

T. Hastie, R. Tibshirani and J. Friedman. Elements of Statistical Learning Ed. 2, Springer, 2009.

Full API documentation: GradientBoostingRegressorScikitsLearnNode

class mdp.nodes.OrthogonalMatchingPursuitScikitsLearnNode

Orthogonal Matching Pursuit model (OMP) This node has been automatically generated by wrapping the sklearn.linear_model.omp.OrthogonalMatchingPursuit class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Read more in the User Guide.

Parameters

n_nonzero_coefs : int, optional
Desired number of non-zero entries in the solution. If None (by default) this value is set to 10% of n_features.
tol : float, optional
Maximum norm of the residual. If not None, overrides n_nonzero_coefs.
fit_intercept : boolean, optional
whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (e.g. data is expected to be already centered).
normalize : boolean, optional, default True
This parameter is ignored when fit_intercept is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use sklearn.preprocessing.StandardScaler before calling fit on an estimator with normalize=False.
precompute : {True, False, ‘auto’}, default ‘auto’
Whether to use a precomputed Gram and Xy matrix to speed up calculations. Improves performance when n_targets or n_samples is very large. Note that if you already have such matrices, you can pass them directly to the fit method.

Attributes

coef_ : array, shape (n_features,) or (n_targets, n_features)
parameter vector (w in the formula)
intercept_ : float or array, shape (n_targets,)
independent term in decision function.
n_iter_ : int or array-like
Number of active features across every target.

Examples

>>> from sklearn.linear_model import OrthogonalMatchingPursuit
>>> from sklearn.datasets import make_regression
>>> X, y = make_regression(noise=4, random_state=0)
>>> reg = OrthogonalMatchingPursuit().fit(X, y)
>>> reg.score(X, y) 
0.9991...
>>> reg.predict(X[:1,])
array([-78.3854...])

Notes

Orthogonal matching pursuit was introduced in G. Mallat, Z. Zhang, Matching pursuits with time-frequency dictionaries, IEEE Transactions on Signal Processing, Vol. 41, No. 12. (December 1993), pp. 3397-3415. (http://blanche.polytechnique.fr/~mallat/papiers/MallatPursuit93.pdf)

This implementation is based on Rubinstein, R., Zibulevsky, M. and Elad, M., Efficient Implementation of the K-SVD Algorithm using Batch Orthogonal Matching Pursuit Technical Report - CS Technion, April 2008. http://www.cs.technion.ac.il/~ronrubin/Publications/KSVD-OMP-v2.pdf

See also

orthogonal_mp orthogonal_mp_gram lars_path Lars LassoLars decomposition.sparse_encode OrthogonalMatchingPursuitCV

Full API documentation: OrthogonalMatchingPursuitScikitsLearnNode

class mdp.nodes.PLSCanonicalScikitsLearnNode

PLSCanonical implements the 2 blocks canonical PLS of the original Wold algorithm [Tenenhaus 1998] p.204, referred as PLS-C2A in [Wegelin 2000]. This node has been automatically generated by wrapping the sklearn.cross_decomposition.pls_.PLSCanonical class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. This class inherits from PLS with mode=”A” and deflation_mode=”canonical”, norm_y_weights=True and algorithm=”nipals”, but svd should provide similar results up to numerical errors.

Read more in the User Guide.

Parameters

n_components : int, (default 2).
Number of components to keep
scale : boolean, (default True)
Option to scale data
algorithm : string, “nipals” or “svd”
The algorithm used to estimate the weights. It will be called n_components times, i.e. once for each iteration of the outer loop.
max_iter : an integer, (default 500)
the maximum number of iterations of the NIPALS inner loop (used only if algorithm=”nipals”)
tol : non-negative real, default 1e-06
the tolerance used in the iterative algorithm
copy : boolean, default True
Whether the deflation should be done on a copy. Let the default value to True unless you don’t care about side effect

Attributes

x_weights_ : array, shape = [p, n_components]
X block weights vectors.
y_weights_ : array, shape = [q, n_components]
Y block weights vectors.
x_loadings_ : array, shape = [p, n_components]
X block loadings vectors.
y_loadings_ : array, shape = [q, n_components]
Y block loadings vectors.
x_scores_ : array, shape = [n_samples, n_components]
X scores.
y_scores_ : array, shape = [n_samples, n_components]
Y scores.
x_rotations_ : array, shape = [p, n_components]
X block to latents rotations.
y_rotations_ : array, shape = [q, n_components]
Y block to latents rotations.
n_iter_ : array-like
Number of iterations of the NIPALS inner loop for each component. Not useful if the algorithm provided is “svd”.

Notes

Matrices:

T: ``x_scores_``
U: ``y_scores_``
W: ``x_weights_``
C: ``y_weights_``
P: ``x_loadings_``
Q: ``y_loadings__``

Are computed such that:

X = T P.T + Err and Y = U Q.T + Err
T[:, k] = Xk W[:, k] for k in range(n_components)
U[:, k] = Yk C[:, k] for k in range(n_components)
``x_rotations_`` = W (P.T W)^(-1)
``y_rotations_`` = C (Q.T C)^(-1)

where Xk and Yk are residual matrices at iteration k.

Slides explaining PLS

For each component k, find weights u, v that optimize:

max corr(Xk u, Yk v) * std(Xk u) std(Yk u), such that ``|u| = |v| = 1``

Note that it maximizes both the correlations between the scores and the intra-block variances.

The residual matrix of X (Xk+1) block is obtained by the deflation on the current X score: x_score.

The residual matrix of Y (Yk+1) block is obtained by deflation on the current Y score. This performs a canonical symmetric version of the PLS regression. But slightly different than the CCA. This is mostly used for modeling.

This implementation provides the same results that the “plspm” package provided in the R language (R-project), using the function plsca(X, Y). Results are equal or collinear with the function pls(..., mode = "canonical") of the “mixOmics” package. The difference relies in the fact that mixOmics implementation does not exactly implement the Wold algorithm since it does not normalize y_weights to one.

Examples

>>> from sklearn.cross_decomposition import PLSCanonical
>>> X = [[0., 0., 1.], [1.,0.,0.], [2.,2.,2.], [2.,5.,4.]]
>>> Y = [[0.1, -0.2], [0.9, 1.1], [6.2, 5.9], [11.9, 12.3]]
>>> plsca = PLSCanonical(n_components=2)
>>> plsca.fit(X, Y)
... 
PLSCanonical(algorithm='nipals', copy=True, max_iter=500, n_components=2,
             scale=True, tol=1e-06)
>>> X_c, Y_c = plsca.transform(X, Y)

References

Jacob A. Wegelin. A survey of Partial Least Squares (PLS) methods, with emphasis on the two-block case. Technical Report 371, Department of Statistics, University of Washington, Seattle, 2000.

Tenenhaus, M. (1998). La regression PLS: theorie et pratique. Paris:

Editions Technic.

See also

CCA PLSSVD

Full API documentation: PLSCanonicalScikitsLearnNode

class mdp.nodes.FeatureAgglomerationScikitsLearnNode

Agglomerate features. This node has been automatically generated by wrapping the sklearn.cluster.hierarchical.FeatureAgglomeration class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Similar to AgglomerativeClustering, but recursively merges features instead of samples.

Read more in the User Guide.

Parameters

n_clusters : int, default 2
The number of clusters to find.
affinity : string or callable, default “euclidean”
Metric used to compute the linkage. Can be “euclidean”, “l1”, “l2”, “manhattan”, “cosine”, or ‘precomputed’. If linkage is “ward”, only “euclidean” is accepted.
memory : None, str or object with the joblib.Memory interface, optional
Used to cache the output of the computation of the tree. By default, no caching is done. If a string is given, it is the path to the caching directory.
connectivity : array-like or callable, optional
Connectivity matrix. Defines for each feature the neighboring features following a given structure of the data. This can be a connectivity matrix itself or a callable that transforms the data into a connectivity matrix, such as derived from kneighbors_graph. Default is None, i.e, the hierarchical clustering algorithm is unstructured.
compute_full_tree : bool or ‘auto’, optional, default “auto”
Stop early the construction of the tree at n_clusters. This is useful to decrease computation time if the number of clusters is not small compared to the number of features. This option is useful only when specifying a connectivity matrix. Note also that when varying the number of clusters and using caching, it may be advantageous to compute the full tree.
linkage : {“ward”, “complete”, “average”, “single”}, optional (default=”ward”)

Which linkage criterion to use. The linkage criterion determines which distance to use between sets of features. The algorithm will merge the pairs of cluster that minimize this criterion.

  • ward minimizes the variance of the clusters being merged.
  • average uses the average of the distances of each feature of the two sets.
  • complete or maximum linkage uses the maximum distances between all features of the two sets.
  • single uses the minimum of the distances between all observations of the two sets.
pooling_func : callable, default np.mean
This combines the values of agglomerated features into a single value, and should accept an array of shape [M, N] and the keyword argument axis=1, and reduce it to an array of size [M].

Attributes

labels_ : array-like, (n_features,)
cluster labels for each feature.
n_leaves_ : int
Number of leaves in the hierarchical tree.
n_components_ : int
The estimated number of connected components in the graph.
children_ : array-like, shape (n_nodes-1, 2)
The children of each non-leaf node. Values less than n_features correspond to leaves of the tree which are the original samples. A node i greater than or equal to n_features is a non-leaf node and has children children_[i - n_features]. Alternatively at the i-th iteration, children[i][0] and children[i][1] are merged to form node n_features + i

Examples

>>> import numpy as np
>>> from sklearn import datasets, cluster
>>> digits = datasets.load_digits()
>>> images = digits.images
>>> X = np.reshape(images, (len(images), -1))
>>> agglo = cluster.FeatureAgglomeration(n_clusters=32)
>>> agglo.fit(X) 
FeatureAgglomeration(affinity='euclidean', compute_full_tree='auto',
           connectivity=None, linkage='ward', memory=None, n_clusters=32,
           pooling_func=...)
>>> X_reduced = agglo.transform(X)
>>> X_reduced.shape
(1797, 32)

Full API documentation: FeatureAgglomerationScikitsLearnNode

class mdp.nodes.SelectPercentileScikitsLearnNode

Select features according to a percentile of the highest scores. This node has been automatically generated by wrapping the sklearn.feature_selection.univariate_selection.SelectPercentile class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Read more in the User Guide.

Parameters

score_func : callable
Function taking two arrays X and y, and returning a pair of arrays (scores, pvalues) or a single array with scores. Default is f_classif (see below “See also”). The default function only works with classification tasks.
percentile : int, optional, default=10
Percent of features to keep.

Attributes

scores_ : array-like, shape=(n_features,)
Scores of features.
pvalues_ : array-like, shape=(n_features,)
p-values of feature scores, None if score_func returned only scores.

Examples

>>> from sklearn.datasets import load_digits
>>> from sklearn.feature_selection import SelectPercentile, chi2
>>> X, y = load_digits(return_X_y=True)
>>> X.shape
(1797, 64)
>>> X_new = SelectPercentile(chi2, percentile=10).fit_transform(X, y)
>>> X_new.shape
(1797, 7)

Notes

Ties between features with equal scores will be broken in an unspecified way.

See also

f_classif: ANOVA F-value between label/feature for classification tasks. mutual_info_classif: Mutual information for a discrete target. chi2: Chi-squared stats of non-negative features for classification tasks. f_regression: F-value between label/feature for regression tasks. mutual_info_regression: Mutual information for a continuous target. SelectKBest: Select features based on the k highest scores. SelectFpr: Select features based on a false positive rate test. SelectFdr: Select features based on an estimated false discovery rate. SelectFwe: Select features based on family-wise error rate. GenericUnivariateSelect: Univariate feature selector with configurable mode.

Full API documentation: SelectPercentileScikitsLearnNode

class mdp.nodes.KernelRidgeScikitsLearnNode

Kernel ridge regression. This node has been automatically generated by wrapping the sklearn.kernel_ridge.KernelRidge class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Kernel ridge regression (KRR) combines ridge regression (linear least squares with l2-norm regularization) with the kernel trick. It thus learns a linear function in the space induced by the respective kernel and the data. For non-linear kernels, this corresponds to a non-linear function in the original space.

The form of the model learned by KRR is identical to support vector regression (SVR). However, different loss functions are used: KRR uses squared error loss while support vector regression uses epsilon-insensitive loss, both combined with l2 regularization. In contrast to SVR, fitting a KRR model can be done in closed-form and is typically faster for medium-sized datasets. On the other hand, the learned model is non-sparse and thus slower than SVR, which learns a sparse model for epsilon > 0, at prediction-time.

This estimator has built-in support for multi-variate regression (i.e., when y is a 2d-array of shape [n_samples, n_targets]).

Read more in the User Guide.

Parameters

alpha : {float, array-like}, shape = [n_targets]
Small positive values of alpha improve the conditioning of the problem and reduce the variance of the estimates. Alpha corresponds to (2*C)^-1 in other linear models such as LogisticRegression or LinearSVC. If an array is passed, penalties are assumed to be specific to the targets. Hence they must correspond in number.
kernel : string or callable, default=”linear”
Kernel mapping used internally. A callable should accept two arguments and the keyword arguments passed to this object as kernel_params, and should return a floating point number. Set to “precomputed” in order to pass a precomputed kernel matrix to the estimator methods instead of samples.
gamma : float, default=None
Gamma parameter for the RBF, laplacian, polynomial, exponential chi2 and sigmoid kernels. Interpretation of the default value is left to the kernel; see the documentation for sklearn.metrics.pairwise. Ignored by other kernels.
degree : float, default=3
Degree of the polynomial kernel. Ignored by other kernels.
coef0 : float, default=1
Zero coefficient for polynomial and sigmoid kernels. Ignored by other kernels.
kernel_params : mapping of string to any, optional
Additional parameters (keyword arguments) for kernel function passed as callable object.

Attributes

dual_coef_ : array, shape = [n_samples] or [n_samples, n_targets]
Representation of weight vector(s) in kernel space
X_fit_ : {array-like, sparse matrix}, shape = [n_samples, n_features]
Training data, which is also required for prediction. If kernel == “precomputed” this is instead the precomputed training matrix, shape = [n_samples, n_samples].

References

  • Kevin P. Murphy “Machine Learning: A Probabilistic Perspective”, The MIT Press chapter 14.4.3, pp. 492-493

See also

sklearn.linear_model.Ridge:

  • Linear ridge regression.

sklearn.svm.SVR:

  • Support Vector Regression implemented using libsvm.

Examples

>>> from sklearn.kernel_ridge import KernelRidge
>>> import numpy as np
>>> n_samples, n_features = 10, 5
>>> rng = np.random.RandomState(0)
>>> y = rng.randn(n_samples)
>>> X = rng.randn(n_samples, n_features)
>>> clf = KernelRidge(alpha=1.0)
>>> clf.fit(X, y) 
KernelRidge(alpha=1.0, coef0=1, degree=3, gamma=None, kernel='linear',
            kernel_params=None)

Full API documentation: KernelRidgeScikitsLearnNode

class mdp.nodes.MultiTaskLassoCVScikitsLearnNode

Multi-task Lasso model trained with L1/L2 mixed-norm as regularizer. This node has been automatically generated by wrapping the sklearn.linear_model.coordinate_descent.MultiTaskLassoCV class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. See glossary entry for cross-validation estimator.

The optimization objective for MultiTaskLasso is:

(1 / (2 * n_samples)) * ||Y - XW||^Fro_2 + alpha * ||W||_21

Where:

||W||_21 = \sum_i \sqrt{\sum_j w_{ij}^2}

i.e. the sum of norm of each row.

Read more in the User Guide.

Parameters

eps : float, optional
Length of the path. eps=1e-3 means that alpha_min / alpha_max = 1e-3.
n_alphas : int, optional
Number of alphas along the regularization path
alphas : array-like, optional
List of alphas where to compute the models. If not provided, set automatically.
fit_intercept : boolean
whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (e.g. data is expected to be already centered).
normalize : boolean, optional, default False
This parameter is ignored when fit_intercept is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use sklearn.preprocessing.StandardScaler before calling fit on an estimator with normalize=False.
max_iter : int, optional
The maximum number of iterations.
tol : float, optional
The tolerance for the optimization: if the updates are smaller than tol, the optimization code checks the dual gap for optimality and continues until it is smaller than tol.
copy_X : boolean, optional, default True
If True, X will be copied; else, it may be overwritten.
cv : int, cross-validation generator or an iterable, optional

Determines the cross-validation splitting strategy. Possible inputs for cv are:

  • None, to use the default 3-fold cross-validation,
  • integer, to specify the number of folds.
  • CV splitter,
  • An iterable yielding (train, test) splits as arrays of indices.

For integer/None inputs, KFold is used.

Refer User Guide for the various cross-validation strategies that can be used here.

Changed in version 0.20: cv default value if None will change from 3-fold to 5-fold in v0.22.

verbose : bool or integer
Amount of verbosity.
n_jobs : int or None, optional (default=None)
Number of CPUs to use during the cross validation. Note that this is used only if multiple values for l1_ratio are given. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
random_state : int, RandomState instance or None, optional, default None
The seed of the pseudo random number generator that selects a random feature to update. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random. Used when selection == ‘random’
selection : str, default ‘cyclic’
If set to ‘random’, a random coefficient is updated every iteration rather than looping over features sequentially by default. This (setting to ‘random’) often leads to significantly faster convergence especially when tol is higher than 1e-4.

Attributes

intercept_ : array, shape (n_tasks,)
Independent term in decision function.
coef_ : array, shape (n_tasks, n_features)
Parameter vector (W in the cost function formula). Note that coef_ stores the transpose of W, W.T.
alpha_ : float
The amount of penalization chosen by cross validation
mse_path_ : array, shape (n_alphas, n_folds)
mean square error for the test set on each fold, varying alpha
alphas_ : numpy array, shape (n_alphas,)
The grid of alphas used for fitting.
n_iter_ : int
number of iterations run by the coordinate descent solver to reach the specified tolerance for the optimal alpha.

Examples

>>> from sklearn.linear_model import MultiTaskLassoCV
>>> from sklearn.datasets import make_regression
>>> X, y = make_regression(n_targets=2, noise=4, random_state=0)
>>> reg = MultiTaskLassoCV(cv=5, random_state=0).fit(X, y)
>>> reg.score(X, y) 
0.9994...
>>> reg.alpha_
0.5713...
>>> reg.predict(X[:1,])
array([[153.7971...,  94.9015...]])

See also

MultiTaskElasticNet ElasticNetCV MultiTaskElasticNetCV

Notes

The algorithm used to fit the model is coordinate descent.

To avoid unnecessary memory duplication the X argument of the fit method should be directly passed as a Fortran-contiguous numpy array.

Full API documentation: MultiTaskLassoCVScikitsLearnNode

class mdp.nodes.GaussianNBScikitsLearnNode

Gaussian Naive Bayes (GaussianNB) This node has been automatically generated by wrapping the sklearn.naive_bayes.GaussianNB class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Can perform online updates to model parameters via partial_fit method. For details on algorithm used to update feature means and variance online, see Stanford CS tech report STAN-CS-79-773 by Chan, Golub, and LeVeque:

Read more in the User Guide.

Parameters

priors : array-like, shape (n_classes,)
Prior probabilities of the classes. If specified the priors are not adjusted according to the data.
var_smoothing : float, optional (default=1e-9)
Portion of the largest variance of all features that is added to variances for calculation stability.

Attributes

class_prior_ : array, shape (n_classes,)
probability of each class.
class_count_ : array, shape (n_classes,)
number of training samples observed in each class.
theta_ : array, shape (n_classes, n_features)
mean of each feature per class
sigma_ : array, shape (n_classes, n_features)
variance of each feature per class
epsilon_ : float
absolute additive value to variances

Examples

>>> import numpy as np
>>> X = np.array([[-1, -1], [-2, -1], [-3, -2], [1, 1], [2, 1], [3, 2]])
>>> Y = np.array([1, 1, 1, 2, 2, 2])
>>> from sklearn.naive_bayes import GaussianNB
>>> clf = GaussianNB()
>>> clf.fit(X, Y)
GaussianNB(priors=None, var_smoothing=1e-09)
>>> print(clf.predict([[-0.8, -1]]))
[1]
>>> clf_pf = GaussianNB()
>>> clf_pf.partial_fit(X, Y, np.unique(Y))
GaussianNB(priors=None, var_smoothing=1e-09)
>>> print(clf_pf.predict([[-0.8, -1]]))
[1]

Full API documentation: GaussianNBScikitsLearnNode

class mdp.nodes.LabelSpreadingScikitsLearnNode

LabelSpreading model for semi-supervised learning This node has been automatically generated by wrapping the sklearn.semi_supervised.label_propagation.LabelSpreading class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. This model is similar to the basic Label Propagation algorithm, but uses affinity matrix based on the normalized graph Laplacian and soft clamping across the labels.

Read more in the User Guide.

Parameters

kernel : {‘knn’, ‘rbf’, callable}
String identifier for kernel function to use or the kernel function itself. Only ‘rbf’ and ‘knn’ strings are valid inputs. The function passed should take two inputs, each of shape [n_samples, n_features], and return a [n_samples, n_samples] shaped weight matrix
gamma : float
parameter for rbf kernel
n_neighbors : integer > 0
parameter for knn kernel
alpha : float
Clamping factor. A value in (0, 1) that specifies the relative amount that an instance should adopt the information from its neighbors as opposed to its initial label. alpha=0 means keeping the initial label information; alpha=1 means replacing all initial information.
max_iter : integer
maximum number of iterations allowed
tol : float
Convergence tolerance: threshold to consider the system at steady state
n_jobs : int or None, optional (default=None)
The number of parallel jobs to run. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.

Attributes

X_ : array, shape = [n_samples, n_features]
Input array.
classes_ : array, shape = [n_classes]
The distinct labels used in classifying instances.
label_distributions_ : array, shape = [n_samples, n_classes]
Categorical distribution for each item.
transduction_ : array, shape = [n_samples]
Label assigned to each item via the transduction.
n_iter_ : int
Number of iterations run.

Examples

>>> import numpy as np
>>> from sklearn import datasets
>>> from sklearn.semi_supervised import LabelSpreading
>>> label_prop_model = LabelSpreading()
>>> iris = datasets.load_iris()
>>> rng = np.random.RandomState(42)
>>> random_unlabeled_points = rng.rand(len(iris.target)) < 0.3
>>> labels = np.copy(iris.target)
>>> labels[random_unlabeled_points] = -1
>>> label_prop_model.fit(iris.data, labels)
... 
LabelSpreading(...)

References

Dengyong Zhou, Olivier Bousquet, Thomas Navin Lal, Jason Weston, Bernhard Schoelkopf. Learning with local and global consistency (2004) http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.115.3219

See Also

LabelPropagation : Unregularized graph based semi-supervised learning

Full API documentation: LabelSpreadingScikitsLearnNode

class mdp.nodes.LatentDirichletAllocationScikitsLearnNode

Latent Dirichlet Allocation with online variational Bayes algorithm This node has been automatically generated by wrapping the sklearn.decomposition.online_lda.LatentDirichletAllocation class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. .. versionadded:: 0.17

Read more in the User Guide.

Parameters

n_components : int, optional (default=10)
Number of topics.
doc_topic_prior : float, optional (default=None)
Prior of document topic distribution theta. If the value is None, defaults to 1 / n_components. In [1]_, this is called alpha.
topic_word_prior : float, optional (default=None)
Prior of topic word distribution beta. If the value is None, defaults to 1 / n_components. In [1]_, this is called eta.
learning_method : ‘batch’ | ‘online’, default=’batch’

Method used to update _component. Only used in fit method. In general, if the data size is large, the online update will be much faster than the batch update.

Valid options:

'batch': Batch variational Bayes method. Use all training data in
    each EM update.
    Old `components_` will be overwritten in each iteration.
'online': Online variational Bayes method. In each EM update, use
    mini-batch of training data to update the ``components_``
    variable incrementally. The learning rate is controlled by the
    ``learning_decay`` and the ``learning_offset`` parameters.

Changed in version 0.20: The default learning method is now "batch".

learning_decay : float, optional (default=0.7)
It is a parameter that control learning rate in the online learning method. The value should be set between (0.5, 1.0] to guarantee asymptotic convergence. When the value is 0.0 and batch_size is n_samples, the update method is same as batch learning. In the literature, this is called kappa.
learning_offset : float, optional (default=10.)
A (positive) parameter that downweights early iterations in online learning. It should be greater than 1.0. In the literature, this is called tau_0.
max_iter : integer, optional (default=10)
The maximum number of iterations.
batch_size : int, optional (default=128)
Number of documents to use in each EM iteration. Only used in online learning.
evaluate_every : int, optional (default=0)
How often to evaluate perplexity. Only used in fit method. set it to 0 or negative number to not evalute perplexity in training at all. Evaluating perplexity can help you check convergence in training process, but it will also increase total training time. Evaluating perplexity in every iteration might increase training time up to two-fold.
total_samples : int, optional (default=1e6)
Total number of documents. Only used in the partial_fit method.
perp_tol : float, optional (default=1e-1)
Perplexity tolerance in batch learning. Only used when evaluate_every is greater than 0.
mean_change_tol : float, optional (default=1e-3)
Stopping tolerance for updating document topic distribution in E-step.
max_doc_update_iter : int (default=100)
Max number of iterations for updating document topic distribution in the E-step.
n_jobs : int or None, optional (default=None)
The number of jobs to use in the E-step. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
verbose : int, optional (default=0)
Verbosity level.
random_state : int, RandomState instance or None, optional (default=None)
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.
n_topics : int, optional (default=None)
This parameter has been renamed to n_components and will be removed in version 0.21. .. deprecated:: 0.19

Attributes

components_ : array, [n_components, n_features]

Variational parameters for topic word distribution. Since the complete conditional for topic word distribution is a Dirichlet, components_[i, j] can be viewed as pseudocount that represents the number of times word j was assigned to topic i. It can also be viewed as distribution over the words for each topic after normalization:

  • model.components_ / model.components_.sum(axis=1)[:, np.newaxis].
n_batch_iter_ : int
Number of iterations of the EM step.
n_iter_ : int
Number of passes over the dataset.

Examples

>>> from sklearn.decomposition import LatentDirichletAllocation
>>> from sklearn.datasets import make_multilabel_classification
>>> # This produces a feature matrix of token counts, similar to what
>>> # CountVectorizer would produce on text.
>>> X, _ = make_multilabel_classification(random_state=0)
>>> lda = LatentDirichletAllocation(n_components=5,
...     random_state=0)
>>> lda.fit(X) 
LatentDirichletAllocation(...)
>>> # get topics for some given samples:
>>> lda.transform(X[-2:])
array([[0.00360392, 0.25499205, 0.0036211 , 0.64236448, 0.09541846],
       [0.15297572, 0.00362644, 0.44412786, 0.39568399, 0.003586  ]])

References

[1] “Online Learning for Latent Dirichlet Allocation”, Matthew D. Hoffman,
David M. Blei, Francis Bach, 2010
[2] “Stochastic Variational Inference”, Matthew D. Hoffman, David M. Blei,
Chong Wang, John Paisley, 2013

[3] Matthew D. Hoffman’s onlineldavb code. Link:

Full API documentation: LatentDirichletAllocationScikitsLearnNode

class mdp.nodes.NMFScikitsLearnNode

Non-Negative Matrix Factorization (NMF) This node has been automatically generated by wrapping the sklearn.decomposition.nmf.NMF class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Find two non-negative matrices (W, H) whose product approximates the non- negative matrix X. This factorization can be used for example for dimensionality reduction, source separation or topic extraction.

The objective function is:

0.5 * ||X - WH||_Fro^2
+ alpha * l1_ratio * ||vec(W)||_1
+ alpha * l1_ratio * ||vec(H)||_1
+ 0.5 * alpha * (1 - l1_ratio) * ||W||_Fro^2
+ 0.5 * alpha * (1 - l1_ratio) * ||H||_Fro^2

Where:

||A||_Fro^2 = \sum_{i,j} A_{ij}^2 (Frobenius norm)
||vec(A)||_1 = \sum_{i,j} abs(A_{ij}) (Elementwise L1 norm)

For multiplicative-update (‘mu’) solver, the Frobenius norm (0.5 * ||X - WH||_Fro^2) can be changed into another beta-divergence loss, by changing the beta_loss parameter.

The objective function is minimized with an alternating minimization of W and H.

Read more in the User Guide.

Parameters

n_components : int or None
Number of components, if n_components is not set all features are kept.
init : ‘random’ | ‘nndsvd’ | ‘nndsvda’ | ‘nndsvdar’ | ‘custom’

Method used to initialize the procedure. Default: ‘nndsvd’ if n_components < n_features, otherwise random. Valid options:

  • ‘random’: non-negative random matrices, scaled with:

    • sqrt(X.mean() / n_components)
  • ‘nndsvd’: Nonnegative Double Singular Value Decomposition (NNDSVD)

    initialization (better for sparseness)

  • ‘nndsvda’: NNDSVD with zeros filled with the average of X

    (better when sparsity is not desired)

  • ‘nndsvdar’: NNDSVD with zeros filled with small random values

    (generally faster, less accurate alternative to NNDSVDa for when sparsity is not desired)

  • ‘custom’: use custom matrices W and H

solver : ‘cd’ | ‘mu’

Numerical solver to use:

  • ‘cd’ is a Coordinate Descent solver.
  • ‘mu’ is a Multiplicative Update solver.

New in version 0.17: Coordinate Descent solver.

New in version 0.19: Multiplicative Update solver.

beta_loss : float or string, default ‘frobenius’

String must be in {‘frobenius’, ‘kullback-leibler’, ‘itakura-saito’}. Beta divergence to be minimized, measuring the distance between X and the dot product WH. Note that values different from ‘frobenius’ (or 2) and ‘kullback-leibler’ (or 1) lead to significantly slower fits. Note that for beta_loss <= 0 (or ‘itakura-saito’), the input matrix X cannot contain zeros. Used only in ‘mu’ solver.

New in version 0.19.

tol : float, default: 1e-4
Tolerance of the stopping condition.
max_iter : integer, default: 200
Maximum number of iterations before timing out.
random_state : int, RandomState instance or None, optional, default: None
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.
alpha : double, default: 0.

Constant that multiplies the regularization terms. Set it to zero to have no regularization.

New in version 0.17: alpha used in the Coordinate Descent solver.

l1_ratio : double, default: 0.

The regularization mixing parameter, with 0 <= l1_ratio <= 1. For l1_ratio = 0 the penalty is an elementwise L2 penalty (aka Frobenius Norm). For l1_ratio = 1 it is an elementwise L1 penalty. For 0 < l1_ratio < 1, the penalty is a combination of L1 and L2.

New in version 0.17: Regularization parameter l1_ratio used in the Coordinate Descent solver.

verbose : bool, default=False
Whether to be verbose.
shuffle : boolean, default: False

If true, randomize the order of coordinates in the CD solver.

New in version 0.17: shuffle parameter used in the Coordinate Descent solver.

Attributes

components_ : array, [n_components, n_features]
Factorization matrix, sometimes called ‘dictionary’.
reconstruction_err_ : number
Frobenius norm of the matrix difference, or beta-divergence, between the training data X and the reconstructed data WH from the fitted model.
n_iter_ : int
Actual number of iterations.

Examples

>>> import numpy as np
>>> X = np.array([[1, 1], [2, 1], [3, 1.2], [4, 1], [5, 0.8], [6, 1]])
>>> from sklearn.decomposition import NMF
>>> model = NMF(n_components=2, init='random', random_state=0)
>>> W = model.fit_transform(X)
>>> H = model.components_

References

Cichocki, Andrzej, and P. H. A. N. Anh-Huy. “Fast local algorithms for large scale nonnegative matrix and tensor factorizations.” IEICE transactions on fundamentals of electronics, communications and computer sciences 92.3: 708-721, 2009.

Fevotte, C., & Idier, J. (2011). Algorithms for nonnegative matrix factorization with the beta-divergence. Neural Computation, 23(9).

Full API documentation: NMFScikitsLearnNode

class mdp.nodes.ScaledLogOddsEstimatorScikitsLearnNode

This node has been automatically generated by wrapping the sklearn.ensemble.gradient_boosting.ScaledLogOddsEstimator class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute.

Full API documentation: ScaledLogOddsEstimatorScikitsLearnNode

class mdp.nodes.MaxAbsScalerScikitsLearnNode

Scale each feature by its maximum absolute value. This node has been automatically generated by wrapping the sklearn.preprocessing.data.MaxAbsScaler class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. This estimator scales and translates each feature individually such that the maximal absolute value of each feature in the training set will be 1.0. It does not shift/center the data, and thus does not destroy any sparsity.

This scaler can also be applied to sparse CSR or CSC matrices.

New in version 0.17.

Parameters

copy : boolean, optional, default is True
Set to False to perform inplace scaling and avoid a copy (if the input is already a numpy array).

Attributes

scale_ : ndarray, shape (n_features,)

Per feature relative scaling of the data.

New in version 0.17: scale_ attribute.

max_abs_ : ndarray, shape (n_features,)
Per feature maximum absolute value.
n_samples_seen_ : int
The number of samples processed by the estimator. Will be reset on new calls to fit, but increments across partial_fit calls.

Examples

>>> from sklearn.preprocessing import MaxAbsScaler
>>> X = [[ 1., -1.,  2.],
...      [ 2.,  0.,  0.],
...      [ 0.,  1., -1.]]
>>> transformer = MaxAbsScaler().fit(X)
>>> transformer
MaxAbsScaler(copy=True)
>>> transformer.transform(X)
array([[ 0.5, -1. ,  1. ],
       [ 1. ,  0. ,  0. ],
       [ 0. ,  1. , -0.5]])

See also

maxabs_scale: Equivalent function without the estimator API.

Notes

NaNs are treated as missing values: disregarded in fit, and maintained in transform.

For a comparison of the different scalers, transformers, and normalizers, see examples/preprocessing/plot_all_scaling.py.

Full API documentation: MaxAbsScalerScikitsLearnNode

class mdp.nodes.HashingVectorizerScikitsLearnNode

Convert a collection of text documents to a matrix of token occurrences This node has been automatically generated by wrapping the sklearn.feature_extraction.text.HashingVectorizer class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. It turns a collection of text documents into a scipy.sparse matrix holding token occurrence counts (or binary occurrence information), possibly normalized as token frequencies if norm=’l1’ or projected on the euclidean unit sphere if norm=’l2’.

This text vectorizer implementation uses the hashing trick to find the token string name to feature integer index mapping.

This strategy has several advantages:

  • it is very low memory scalable to large datasets as there is no need to store a vocabulary dictionary in memory
  • it is fast to pickle and un-pickle as it holds no state besides the constructor parameters
  • it can be used in a streaming (partial fit) or parallel pipeline as there is no state computed during fit.

There are also a couple of cons (vs using a CountVectorizer with an in-memory vocabulary):

  • there is no way to compute the inverse transform (from feature indices to string feature names) which can be a problem when trying to introspect which features are most important to a model.
  • there can be collisions: distinct tokens can be mapped to the same feature index. However in practice this is rarely an issue if n_features is large enough (e.g. 2 ** 18 for text classification problems).
  • no IDF weighting as this would render the transformer stateful.

The hash function employed is the signed 32-bit version of Murmurhash3.

Read more in the User Guide.

Parameters

input : string {‘filename’, ‘file’, ‘content’}

If ‘filename’, the sequence passed as an argument to fit is expected to be a list of filenames that need reading to fetch the raw content to analyze.

If ‘file’, the sequence items must have a ‘read’ method (file-like object) that is called to fetch the bytes in memory.

Otherwise the input is expected to be the sequence strings or bytes items are expected to be analyzed directly.

encoding : string, default=’utf-8’
If bytes or files are given to analyze, this encoding is used to decode.
decode_error : {‘strict’, ‘ignore’, ‘replace’}
Instruction on what to do if a byte sequence is given to analyze that contains characters not of the given encoding. By default, it is ‘strict’, meaning that a UnicodeDecodeError will be raised. Other values are ‘ignore’ and ‘replace’.
strip_accents : {‘ascii’, ‘unicode’, None}

Remove accents and perform other character normalization during the preprocessing step. ‘ascii’ is a fast method that only works on characters that have an direct ASCII mapping. ‘unicode’ is a slightly slower method that works on any characters. None (default) does nothing.

Both ‘ascii’ and ‘unicode’ use NFKD normalization from unicodedata.normalize().

lowercase : boolean, default=True
Convert all characters to lowercase before tokenizing.
preprocessor : callable or None (default)
Override the preprocessing (string transformation) stage while preserving the tokenizing and n-grams generation steps.
tokenizer : callable or None (default)
Override the string tokenization step while preserving the preprocessing and n-grams generation steps. Only applies if analyzer == 'word'.
stop_words : string {‘english’}, list, or None (default)

If ‘english’, a built-in stop word list for English is used. There are several known issues with ‘english’ and you should consider an alternative (see stop_words).

If a list, that list is assumed to contain stop words, all of which will be removed from the resulting tokens. Only applies if analyzer == 'word'.

token_pattern : string
Regular expression denoting what constitutes a “token”, only used if analyzer == 'word'. The default regexp selects tokens of 2 or more alphanumeric characters (punctuation is completely ignored and always treated as a token separator).
ngram_range : tuple (min_n, max_n), default=(1, 1)
The lower and upper boundary of the range of n-values for different n-grams to be extracted. All values of n such that min_n <= n <= max_n will be used.
analyzer : string, {‘word’, ‘char’, ‘char_wb’} or callable

Whether the feature should be made of word or character n-grams. Option ‘char_wb’ creates character n-grams only from text inside word boundaries; n-grams at the edges of words are padded with space.

If a callable is passed it is used to extract the sequence of features out of the raw, unprocessed input.

n_features : integer, default=(2 ** 20)
The number of features (columns) in the output matrices. Small numbers of features are likely to cause hash collisions, but large numbers will cause larger coefficient dimensions in linear learners.
binary : boolean, default=False.
If True, all non zero counts are set to 1. This is useful for discrete probabilistic models that model binary events rather than integer counts.
norm : ‘l1’, ‘l2’ or None, optional
Norm used to normalize term vectors. None for no normalization.
alternate_sign : boolean, optional, default True

When True, an alternating sign is added to the features as to approximately conserve the inner product in the hashed space even for small n_features. This approach is similar to sparse random projection.

New in version 0.19.

non_negative : boolean, optional, default False

When True, an absolute value is applied to the features matrix prior to returning it. When used in conjunction with alternate_sign=True, this significantly reduces the inner product preservation property.

Deprecated since version 0.19: This option will be removed in 0.21.

dtype : type, optional
Type of the matrix returned by fit_transform() or transform().

Examples

>>> from sklearn.feature_extraction.text import HashingVectorizer
>>> corpus = [
...     'This is the first document.',
...     'This document is the second document.',
...     'And this is the third one.',
...     'Is this the first document?',
... ]
>>> vectorizer = HashingVectorizer(n_features=2**4)
>>> X = vectorizer.fit_transform(corpus)
>>> print(X.shape)
(4, 16)

See also

CountVectorizer, TfidfVectorizer

Full API documentation: HashingVectorizerScikitsLearnNode

class mdp.nodes.LogisticRegressionCVScikitsLearnNode

Logistic Regression CV (aka logit, MaxEnt) classifier. This node has been automatically generated by wrapping the sklearn.linear_model.logistic.LogisticRegressionCV class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. See glossary entry for cross-validation estimator.

This class implements logistic regression using liblinear, newton-cg, sag of lbfgs optimizer. The newton-cg, sag and lbfgs solvers support only L2 regularization with primal formulation. The liblinear solver supports both L1 and L2 regularization, with a dual formulation only for the L2 penalty.

For the grid of Cs values (that are set by default to be ten values in a logarithmic scale between 1e-4 and 1e4), the best hyperparameter is selected by the cross-validator StratifiedKFold, but it can be changed using the cv parameter. In the case of newton-cg and lbfgs solvers, we warm start along the path i.e guess the initial coefficients of the present fit to be the coefficients got after convergence in the previous fit, so it is supposed to be faster for high-dimensional dense data.

For a multiclass problem, the hyperparameters for each class are computed using the best scores got by doing a one-vs-rest in parallel across all folds and classes. Hence this is not the true multinomial loss.

Read more in the User Guide.

Parameters

Cs : list of floats | int
Each of the values in Cs describes the inverse of regularization strength. If Cs is as an int, then a grid of Cs values are chosen in a logarithmic scale between 1e-4 and 1e4. Like in support vector machines, smaller values specify stronger regularization.
fit_intercept : bool, default: True
Specifies if a constant (a.k.a. bias or intercept) should be added to the decision function.
cv : integer or cross-validation generator, default: None

The default cross-validation generator used is Stratified K-Folds. If an integer is provided, then it is the number of folds used. See the module sklearn.model_selection module for the list of possible cross-validation objects.

Changed in version 0.20: cv default value if None will change from 3-fold to 5-fold in v0.22.

dual : bool
Dual or primal formulation. Dual formulation is only implemented for l2 penalty with liblinear solver. Prefer dual=False when n_samples > n_features.
penalty : str, ‘l1’ or ‘l2’
Used to specify the norm used in the penalization. The ‘newton-cg’, ‘sag’ and ‘lbfgs’ solvers support only l2 penalties.
scoring : string, callable, or None
A string (see model evaluation documentation) or a scorer callable object / function with signature scorer(estimator, X, y). For a list of scoring functions that can be used, look at sklearn.metrics. The default scoring option used is ‘accuracy’.

solver : str, {‘newton-cg’, ‘lbfgs’, ‘liblinear’, ‘sag’, ‘saga’}, default: ‘lbfgs’.

Algorithm to use in the optimization problem.

  • For small datasets, ‘liblinear’ is a good choice, whereas ‘sag’ and ‘saga’ are faster for large ones.
  • For multiclass problems, only ‘newton-cg’, ‘sag’, ‘saga’ and ‘lbfgs’ handle multinomial loss; ‘liblinear’ is limited to one-versus-rest schemes.
  • ‘newton-cg’, ‘lbfgs’ and ‘sag’ only handle L2 penalty, whereas ‘liblinear’ and ‘saga’ handle L1 penalty.
  • ‘liblinear’ might be slower in LogisticRegressionCV because it does not handle warm-starting.

Note that ‘sag’ and ‘saga’ fast convergence is only guaranteed on features with approximately the same scale. You can preprocess the data with a scaler from sklearn.preprocessing.

New in version 0.17: Stochastic Average Gradient descent solver.

New in version 0.19: SAGA solver.

tol : float, optional
Tolerance for stopping criteria.
max_iter : int, optional
Maximum number of iterations of the optimization algorithm.
class_weight : dict or ‘balanced’, optional

Weights associated with classes in the form {class_label: weight}. If not given, all classes are supposed to have weight one.

The “balanced” mode uses the values of y to automatically adjust weights inversely proportional to class frequencies in the input data as n_samples / (n_classes * np.bincount(y)).

Note that these weights will be multiplied with sample_weight (passed through the fit method) if sample_weight is specified.

New in version 0.17: class_weight == ‘balanced’

n_jobs : int or None, optional (default=None)
Number of CPU cores used during the cross-validation loop. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
verbose : int
For the ‘liblinear’, ‘sag’ and ‘lbfgs’ solvers set verbose to any positive number for verbosity.
refit : bool
If set to True, the scores are averaged across all folds, and the coefs and the C that corresponds to the best score is taken, and a final refit is done using these parameters. Otherwise the coefs, intercepts and C that correspond to the best scores across folds are averaged.
intercept_scaling : float, default 1.

Useful only when the solver ‘liblinear’ is used and self.fit_intercept is set to True. In this case, x becomes [x, self.intercept_scaling], i.e. a “synthetic” feature with constant value equal to intercept_scaling is appended to the instance vector. The intercept becomes intercept_scaling * synthetic_feature_weight.

Note! the synthetic feature weight is subject to l1/l2 regularization as all other features. To lessen the effect of regularization on synthetic feature weight (and therefore on the intercept) intercept_scaling has to be increased.

multi_class : str, {‘ovr’, ‘multinomial’, ‘auto’}, default: ‘ovr’

If the option chosen is ‘ovr’, then a binary problem is fit for each label. For ‘multinomial’ the loss minimised is the multinomial loss fit across the entire probability distribution, even when the data is binary. ‘multinomial’ is unavailable when solver=’liblinear’. ‘auto’ selects ‘ovr’ if the data is binary, or if solver=’liblinear’, and otherwise selects ‘multinomial’.

New in version 0.18: Stochastic Average Gradient descent solver for ‘multinomial’ case.

Changed in version 0.20: Default will change from ‘ovr’ to ‘auto’ in 0.22.

random_state : int, RandomState instance or None, optional, default None
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.

Attributes

classes_ : array, shape (n_classes, )
A list of class labels known to the classifier.
coef_ : array, shape (1, n_features) or (n_classes, n_features)

Coefficient of the features in the decision function.

coef_ is of shape (1, n_features) when the given problem is binary.

intercept_ : array, shape (1,) or (n_classes,)

Intercept (a.k.a. bias) added to the decision function.

If fit_intercept is set to False, the intercept is set to zero. intercept_ is of shape(1,) when the problem is binary.

Cs_ : array
Array of C i.e. inverse of regularization parameter values used for cross-validation.
coefs_paths_ : array, shape (n_folds, len(Cs_), n_features) or (n_folds, len(Cs_), n_features + 1)
dict with classes as the keys, and the path of coefficients obtained during cross-validating across each fold and then across each Cs after doing an OvR for the corresponding class as values. If the ‘multi_class’ option is set to ‘multinomial’, then the coefs_paths are the coefficients corresponding to each class. Each dict value has shape (n_folds, len(Cs_), n_features) or (n_folds, len(Cs_), n_features + 1) depending on whether the intercept is fit or not.
scores_ : dict
dict with classes as the keys, and the values as the grid of scores obtained during cross-validating each fold, after doing an OvR for the corresponding class. If the ‘multi_class’ option given is ‘multinomial’ then the same scores are repeated across all classes, since this is the multinomial class. Each dict value has shape (n_folds, len(Cs))
C_ : array, shape (n_classes,) or (n_classes - 1,)
Array of C that maps to the best scores across every class. If refit is set to False, then for each class, the best C is the average of the C’s that correspond to the best scores for each fold. C_ is of shape(n_classes,) when the problem is binary.
n_iter_ : array, shape (n_classes, n_folds, n_cs) or (1, n_folds, n_cs)
Actual number of iterations for all classes, folds and Cs. In the binary or multinomial cases, the first dimension is equal to 1.

Examples

>>> from sklearn.datasets import load_iris
>>> from sklearn.linear_model import LogisticRegressionCV
>>> X, y = load_iris(return_X_y=True)
>>> clf = LogisticRegressionCV(cv=5, random_state=0,
...                            multi_class='multinomial').fit(X, y)
>>> clf.predict(X[:2, :])
array([0, 0])
>>> clf.predict_proba(X[:2, :]).shape
(2, 3)
>>> clf.score(X, y) 
0.98...

See also

LogisticRegression

Full API documentation: LogisticRegressionCVScikitsLearnNode

class mdp.nodes.ZeroEstimatorScikitsLearnNode

This node has been automatically generated by wrapping the sklearn.ensemble.gradient_boosting.ZeroEstimator class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute.

Full API documentation: ZeroEstimatorScikitsLearnNode

class mdp.nodes.SVCScikitsLearnNode

C-Support Vector Classification. This node has been automatically generated by wrapping the sklearn.svm.classes.SVC class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. The implementation is based on libsvm. The fit time complexity is more than quadratic with the number of samples which makes it hard to scale to dataset with more than a couple of 10000 samples.

The multiclass support is handled according to a one-vs-one scheme.

For details on the precise mathematical formulation of the provided kernel functions and how gamma, coef0 and degree affect each other, see the corresponding section in the narrative documentation:

svm_kernels.

Read more in the User Guide.

Parameters

C : float, optional (default=1.0)
Penalty parameter C of the error term.
kernel : string, optional (default=’rbf’)
Specifies the kernel type to be used in the algorithm. It must be one of ‘linear’, ‘poly’, ‘rbf’, ‘sigmoid’, ‘precomputed’ or a callable. If none is given, ‘rbf’ will be used. If a callable is given it is used to pre-compute the kernel matrix from data matrices; that matrix should be an array of shape (n_samples, n_samples).
degree : int, optional (default=3)
Degree of the polynomial kernel function (‘poly’). Ignored by all other kernels.
gamma : float, optional (default=’auto’)

Kernel coefficient for ‘rbf’, ‘poly’ and ‘sigmoid’.

Current default is ‘auto’ which uses 1 / n_features, if gamma='scale' is passed then it uses 1 / (n_features * X.var()) as value of gamma. The current default of gamma, ‘auto’, will change to ‘scale’ in version 0.22. ‘auto_deprecated’, a deprecated version of ‘auto’ is used as a default indicating that no explicit value of gamma was passed.

coef0 : float, optional (default=0.0)
Independent term in kernel function. It is only significant in ‘poly’ and ‘sigmoid’.
shrinking : boolean, optional (default=True)
Whether to use the shrinking heuristic.
probability : boolean, optional (default=False)
Whether to enable probability estimates. This must be enabled prior to calling fit, and will slow down that method.
tol : float, optional (default=1e-3)
Tolerance for stopping criterion.
cache_size : float, optional
Specify the size of the kernel cache (in MB).
class_weight : {dict, ‘balanced’}, optional
Set the parameter C of class i to class_weight[i]*C for SVC. If not given, all classes are supposed to have weight one. The “balanced” mode uses the values of y to automatically adjust weights inversely proportional to class frequencies in the input data as n_samples / (n_classes * np.bincount(y))
verbose : bool, default: False
Enable verbose output. Note that this setting takes advantage of a per-process runtime setting in libsvm that, if enabled, may not work properly in a multithreaded context.
max_iter : int, optional (default=-1)
Hard limit on iterations within solver, or -1 for no limit.
decision_function_shape : ‘ovo’, ‘ovr’, default=’ovr’

Whether to return a one-vs-rest (‘ovr’) decision function of shape (n_samples, n_classes) as all other classifiers, or the original one-vs-one (‘ovo’) decision function of libsvm which has shape (n_samples, n_classes * (n_classes - 1) / 2). However, one-vs-one (‘ovo’) is always used as multi-class strategy.

Changed in version 0.19: decision_function_shape is ‘ovr’ by default.

New in version 0.17: decision_function_shape=’ovr’ is recommended.

Changed in version 0.17: Deprecated decision_function_shape=’ovo’ and None.

random_state : int, RandomState instance or None, optional (default=None)
The seed of the pseudo random number generator used when shuffling the data for probability estimates. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.

Attributes

support_ : array-like, shape = [n_SV]
Indices of support vectors.
support_vectors_ : array-like, shape = [n_SV, n_features]
Support vectors.
n_support_ : array-like, dtype=int32, shape = [n_class]
Number of support vectors for each class.
dual_coef_ : array, shape = [n_class-1, n_SV]
Coefficients of the support vector in the decision function. For multiclass, coefficient for all 1-vs-1 classifiers. The layout of the coefficients in the multiclass case is somewhat non-trivial. See the section about multi-class classification in the SVM section of the User Guide for details.
coef_ : array, shape = [n_class * (n_class-1) / 2, n_features]

Weights assigned to the features (coefficients in the primal problem). This is only available in the case of a linear kernel.

coef_ is a readonly property derived from dual_coef_ and support_vectors_.

intercept_ : array, shape = [n_class * (n_class-1) / 2]
Constants in decision function.
fit_status_ : int
0 if correctly fitted, 1 otherwise (will raise warning)

probA_ : array, shape = [n_class * (n_class-1) / 2] probB_ : array, shape = [n_class * (n_class-1) / 2]

If probability=True, the parameters learned in Platt scaling to produce probability estimates from decision values. If probability=False, an empty array. Platt scaling uses the logistic function 1 / (1 + exp(decision_value * ``probA_ + probB_))`` where probA_ and probB_ are learned from the dataset [2]_. For more information on the multiclass case and training procedure see section 8 of [1]_.

Examples

>>> import numpy as np
>>> X = np.array([[-1, -1], [-2, -1], [1, 1], [2, 1]])
>>> y = np.array([1, 1, 2, 2])
>>> from sklearn.svm import SVC
>>> clf = SVC(gamma='auto')
>>> clf.fit(X, y) 
SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0,
    decision_function_shape='ovr', degree=3, gamma='auto', kernel='rbf',
    max_iter=-1, probability=False, random_state=None, shrinking=True,
    tol=0.001, verbose=False)
>>> print(clf.predict([[-0.8, -1]]))
[1]

See also

SVR
Support Vector Machine for Regression implemented using libsvm.
LinearSVC
Scalable Linear Support Vector Machine for classification implemented using liblinear. Check the See also section of LinearSVC for more comparison element.

References

[1]LIBSVM: A Library for Support Vector Machines
[2]Platt, John (1999). “Probabilistic outputs for support vector machines and comparison to regularizedlikelihood methods.”

Full API documentation: SVCScikitsLearnNode

class mdp.nodes.IsotonicRegressionScikitsLearnNode

Isotonic regression model. This node has been automatically generated by wrapping the sklearn.isotonic.IsotonicRegression class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. The isotonic regression optimization problem is defined by:

min sum w_i (y[i] - y_[i]) ** 2

subject to y_[i] <= y_[j] whenever X[i] <= X[j]
and min(y_) = y_min, max(y_) = y_max

where:

    • y[i] are inputs (real numbers)
    • y_[i] are fitted
    • X specifies the order.
  • If X is non-decreasing then y_ is non-decreasing.
    • w[i] are optional strictly positive weights (default to 1.0)

Read more in the User Guide.

Parameters

y_min : optional, default: None
If not None, set the lowest value of the fit to y_min.
y_max : optional, default: None
If not None, set the highest value of the fit to y_max.
increasing : boolean or string, optional, default: True

If boolean, whether or not to fit the isotonic regression with y increasing or decreasing.

The string value “auto” determines whether y should increase or decrease based on the Spearman correlation estimate’s sign.

out_of_bounds : string, optional, default: “nan”
The out_of_bounds parameter handles how x-values outside of the training domain are handled. When set to “nan”, predicted y-values will be NaN. When set to “clip”, predicted y-values will be set to the value corresponding to the nearest train interval endpoint. When set to “raise”, allow interp1d to throw ValueError.

Attributes

X_min_ : float
Minimum value of input array X_ for left bound.
X_max_ : float
Maximum value of input array X_ for right bound.
f_ : function
The stepwise interpolating function that covers the input domain X.

Notes

Ties are broken using the secondary method from Leeuw, 1977.

References

Isotonic Median Regression: A Linear Programming Approach Nilotpal Chakravarti Mathematics of Operations Research Vol. 14, No. 2 (May, 1989), pp. 303-308

Isotone Optimization in R : Pool-Adjacent-Violators Algorithm (PAVA) and Active Set Methods Leeuw, Hornik, Mair Journal of Statistical Software 2009

Correctness of Kruskal’s algorithms for monotone regression with ties Leeuw, Psychometrica, 1977

Full API documentation: IsotonicRegressionScikitsLearnNode

class mdp.nodes.DictVectorizerScikitsLearnNode

Transforms lists of feature-value mappings to vectors. This node has been automatically generated by wrapping the sklearn.feature_extraction.dict_vectorizer.DictVectorizer class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. This transformer turns lists of mappings (dict-like objects) of feature names to feature values into Numpy arrays or scipy.sparse matrices for use with scikit-learn estimators.

When feature values are strings, this transformer will do a binary one-hot (aka one-of-K) coding: one boolean-valued feature is constructed for each of the possible string values that the feature can take on. For instance, a feature “f” that can take on the values “ham” and “spam” will become two features in the output, one signifying “f=ham”, the other “f=spam”.

However, note that this transformer will only do a binary one-hot encoding when feature values are of type string. If categorical features are represented as numeric values such as int, the DictVectorizer can be followed by sklearn.preprocessing.OneHotEncoder to complete binary one-hot encoding.

Features that do not occur in a sample (mapping) will have a zero value in the resulting array/matrix.

Read more in the User Guide.

Parameters

dtype : callable, optional
The type of feature values. Passed to Numpy array/scipy.sparse matrix constructors as the dtype argument.
separator : string, optional
Separator string used when constructing new features for one-hot coding.
sparse : boolean, optional.
Whether transform should produce scipy.sparse matrices. True by default.
sort : boolean, optional.
Whether feature_names_ and vocabulary_ should be sorted when fitting. True by default.

Attributes

vocabulary_ : dict
A dictionary mapping feature names to feature indices.
feature_names_ : list
A list of length n_features containing the feature names (e.g., “f=ham” and “f=spam”).

Examples

>>> from sklearn.feature_extraction import DictVectorizer
>>> v = DictVectorizer(sparse=False)
>>> D = [{'foo': 1, 'bar': 2}, {'foo': 3, 'baz': 1}]
>>> X = v.fit_transform(D)
>>> X
array([[2., 0., 1.],
       [0., 1., 3.]])
>>> v.inverse_transform(X) ==         [{'bar': 2.0, 'foo': 1.0}, {'baz': 1.0, 'foo': 3.0}]
True
>>> v.transform({'foo': 4, 'unseen_feature': 3})
array([[0., 0., 4.]])

See also

FeatureHasher : performs vectorization using only a hash function. sklearn.preprocessing.OrdinalEncoder : handles nominal/categorical

features encoded as columns of arbitrary data types.

Full API documentation: DictVectorizerScikitsLearnNode

class mdp.nodes.LinearSVCScikitsLearnNode

Linear Support Vector Classification. This node has been automatically generated by wrapping the sklearn.svm.classes.LinearSVC class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Similar to SVC with parameter kernel=’linear’, but implemented in terms of liblinear rather than libsvm, so it has more flexibility in the choice of penalties and loss functions and should scale better to large numbers of samples.

This class supports both dense and sparse input and the multiclass support is handled according to a one-vs-the-rest scheme.

Read more in the User Guide.

Parameters

penalty : string, ‘l1’ or ‘l2’ (default=’l2’)
Specifies the norm used in the penalization. The ‘l2’ penalty is the standard used in SVC. The ‘l1’ leads to coef_ vectors that are sparse.
loss : string, ‘hinge’ or ‘squared_hinge’ (default=’squared_hinge’)
Specifies the loss function. ‘hinge’ is the standard SVM loss (used e.g. by the SVC class) while ‘squared_hinge’ is the square of the hinge loss.
dual : bool, (default=True)
Select the algorithm to either solve the dual or primal optimization problem. Prefer dual=False when n_samples > n_features.
tol : float, optional (default=1e-4)
Tolerance for stopping criteria.
C : float, optional (default=1.0)
Penalty parameter C of the error term.
multi_class : string, ‘ovr’ or ‘crammer_singer’ (default=’ovr’)
Determines the multi-class strategy if y contains more than two classes. "ovr" trains n_classes one-vs-rest classifiers, while "crammer_singer" optimizes a joint objective over all classes. While crammer_singer is interesting from a theoretical perspective as it is consistent, it is seldom used in practice as it rarely leads to better accuracy and is more expensive to compute. If "crammer_singer" is chosen, the options loss, penalty and dual will be ignored.
fit_intercept : boolean, optional (default=True)
Whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (i.e. data is expected to be already centered).
intercept_scaling : float, optional (default=1)
When self.fit_intercept is True, instance vector x becomes [x, self.intercept_scaling], i.e. a “synthetic” feature with constant value equals to intercept_scaling is appended to the instance vector. The intercept becomes intercept_scaling * synthetic feature weight Note! the synthetic feature weight is subject to l1/l2 regularization as all other features. To lessen the effect of regularization on synthetic feature weight (and therefore on the intercept) intercept_scaling has to be increased.
class_weight : {dict, ‘balanced’}, optional
Set the parameter C of class i to class_weight[i]*C for SVC. If not given, all classes are supposed to have weight one. The “balanced” mode uses the values of y to automatically adjust weights inversely proportional to class frequencies in the input data as n_samples / (n_classes * np.bincount(y))
verbose : int, (default=0)
Enable verbose output. Note that this setting takes advantage of a per-process runtime setting in liblinear that, if enabled, may not work properly in a multithreaded context.
random_state : int, RandomState instance or None, optional (default=None)
The seed of the pseudo random number generator to use when shuffling the data for the dual coordinate descent (if dual=True). When dual=False the underlying implementation of LinearSVC is not random and random_state has no effect on the results. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.
max_iter : int, (default=1000)
The maximum number of iterations to be run.

Attributes

coef_ : array, shape = [n_features] if n_classes == 2 else [n_classes, n_features]

Weights assigned to the features (coefficients in the primal problem). This is only available in the case of a linear kernel.

coef_ is a readonly property derived from raw_coef_ that follows the internal memory layout of liblinear.

intercept_ : array, shape = [1] if n_classes == 2 else [n_classes]
Constants in decision function.

Examples

>>> from sklearn.svm import LinearSVC
>>> from sklearn.datasets import make_classification
>>> X, y = make_classification(n_features=4, random_state=0)
>>> clf = LinearSVC(random_state=0, tol=1e-5)
>>> clf.fit(X, y)
LinearSVC(C=1.0, class_weight=None, dual=True, fit_intercept=True,
     intercept_scaling=1, loss='squared_hinge', max_iter=1000,
     multi_class='ovr', penalty='l2', random_state=0, tol=1e-05, verbose=0)
>>> print(clf.coef_)
[[0.085... 0.394... 0.498... 0.375...]]
>>> print(clf.intercept_)
[0.284...]
>>> print(clf.predict([[0, 0, 0, 0]]))
[1]

Notes

The underlying C implementation uses a random number generator to select features when fitting the model. It is thus not uncommon to have slightly different results for the same input data. If that happens, try with a smaller tol parameter.

The underlying implementation, liblinear, uses a sparse internal representation for the data that will incur a memory copy.

Predict output may not match that of standalone liblinear in certain cases. See differences from liblinear in the narrative documentation.

References

LIBLINEAR: A Library for Large Linear Classification

See also

SVC

Implementation of Support Vector Machine classifier using libsvm:

  • the kernel can be non-linear but its SMO algorithm does not
  • scale to large number of samples as LinearSVC does.

Furthermore SVC multi-class mode is implemented using one vs one scheme while LinearSVC uses one vs the rest. It is possible to implement one vs the rest with SVC by using the sklearn.multiclass.OneVsRestClassifier wrapper.

Finally SVC can fit dense data without memory copy if the input is C-contiguous. Sparse data will still incur memory copy though.

sklearn.linear_model.SGDClassifier
SGDClassifier can optimize the same cost function as LinearSVC by adjusting the penalty and loss parameters. In addition it requires less memory, allows incremental (online) learning, and implements various loss functions and regularization regimes.

Full API documentation: LinearSVCScikitsLearnNode

class mdp.nodes.RandomizedLassoScikitsLearnNode

Randomized Lasso. This node has been automatically generated by wrapping the sklearn.linear_model.randomized_l1.RandomizedLasso class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Randomized Lasso works by subsampling the training data and computing a Lasso estimate where the penalty of a random subset of coefficients has been scaled. By performing this double randomization several times, the method assigns high scores to features that are repeatedly selected across randomizations. This is known as stability selection. In short, features selected more often are considered good features.

Parameters

alpha : float, ‘aic’, or ‘bic’, optional
The regularization parameter alpha parameter in the Lasso. Warning: this is not the alpha parameter in the stability selection article which is scaling.
scaling : float, optional
The s parameter used to randomly scale the penalty of different features. Should be between 0 and 1.
sample_fraction : float, optional
The fraction of samples to be used in each randomized design. Should be between 0 and 1. If 1, all samples are used.
n_resampling : int, optional
Number of randomized models.
selection_threshold : float, optional
The score above which features should be selected.
fit_intercept : boolean, optional
whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (e.g. data is expected to be already centered).
verbose : boolean or integer, optional
Sets the verbosity amount
normalize : boolean, optional, default True
If True, the regressors X will be normalized before regression. This parameter is ignored when fit_intercept is set to False. When the regressors are normalized, note that this makes the hyperparameters learned more robust and almost independent of the number of samples. The same property is not valid for standardized data. However, if you wish to standardize, please use preprocessing.StandardScaler before calling fit on an estimator with normalize=False.
precompute : True | False | ‘auto’ | array-like
Whether to use a precomputed Gram matrix to speed up calculations. If set to ‘auto’ let us decide. The Gram matrix can also be passed as argument, but it will be used only for the selection of parameter alpha, if alpha is ‘aic’ or ‘bic’.
max_iter : integer, optional
Maximum number of iterations to perform in the Lars algorithm.
eps : float, optional
The machine-precision regularization in the computation of the Cholesky diagonal factors. Increase this for very ill-conditioned systems. Unlike the ‘tol’ parameter in some iterative optimization-based algorithms, this parameter does not control the tolerance of the optimization.
random_state : int, RandomState instance or None, optional (default=None)
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.
n_jobs : int or None, optional (default=None)
Number of CPUs to use during the resampling. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
pre_dispatch : int, or string, optional

Controls the number of jobs that get dispatched during parallel execution. Reducing this number can be useful to avoid an explosion of memory consumption when more jobs get dispatched than CPUs can process. This parameter can be:

  • None, in which case all the jobs are immediately created and spawned. Use this for lightweight and fast-running jobs, to avoid delays due to on-demand spawning of the jobs
  • An int, giving the exact number of total jobs that are spawned
  • A string, giving an expression as a function of n_jobs, as in ‘2*n_jobs’
memory : None, str or object with the joblib.Memory interface, optional (default=None)
Used for internal caching. By default, no caching is done. If a string is given, it is the path to the caching directory.

Attributes

scores_ : array, shape = [n_features]
Feature scores between 0 and 1.
all_scores_ : array, shape = [n_features, n_reg_parameter]
Feature scores between 0 and 1 for all values of the regularization parameter. The reference article suggests scores_ is the max of all_scores_.

Examples

>>> from sklearn.linear_model import RandomizedLasso
>>> randomized_lasso = RandomizedLasso() 

References

Stability selection Nicolai Meinshausen, Peter Buhlmann Journal of the Royal Statistical Society: Series B Volume 72, Issue 4, pages 417-473, September 2010 DOI: 10.1111/j.1467-9868.2010.00740.x

See also

RandomizedLogisticRegression, Lasso, ElasticNet

Full API documentation: RandomizedLassoScikitsLearnNode

class mdp.nodes.MultiLabelBinarizerScikitsLearnNode

Transform between iterable of iterables and a multilabel format This node has been automatically generated by wrapping the sklearn.preprocessing.label.MultiLabelBinarizer class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Although a list of sets or tuples is a very intuitive format for multilabel data, it is unwieldy to process. This transformer converts between this intuitive format and the supported multilabel format: a (samples x classes) binary matrix indicating the presence of a class label.

Parameters

classes : array-like of shape [n_classes] (optional)
Indicates an ordering for the class labels. All entries should be unique (cannot contain duplicate classes).
sparse_output : boolean (default: False),
Set to true if output binary array is desired in CSR sparse format

Attributes

classes_ : array of labels
A copy of the classes parameter where provided, or otherwise, the sorted set of classes found when fitting.

Examples

>>> from sklearn.preprocessing import MultiLabelBinarizer
>>> mlb = MultiLabelBinarizer()
>>> mlb.fit_transform([(1, 2), (3,)])
array([[1, 1, 0],
       [0, 0, 1]])
>>> mlb.classes_
array([1, 2, 3])
>>> mlb.fit_transform([set(['sci-fi', 'thriller']), set(['comedy'])])
array([[0, 1, 1],
       [1, 0, 0]])
>>> list(mlb.classes_)
['comedy', 'sci-fi', 'thriller']

See also

sklearn.preprocessing.OneHotEncoder : encode categorical features
using a one-hot aka one-of-K scheme.

Full API documentation: MultiLabelBinarizerScikitsLearnNode

class mdp.nodes.FastICAScikitsLearnNode

FastICA: a fast algorithm for Independent Component Analysis. This node has been automatically generated by wrapping the sklearn.decomposition.fastica_.FastICA class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Read more in the User Guide.

Parameters

n_components : int, optional
Number of components to use. If none is passed, all are used.
algorithm : {‘parallel’, ‘deflation’}
Apply parallel or deflational algorithm for FastICA.
whiten : boolean, optional
If whiten is false, the data is already considered to be whitened, and no whitening is performed.
fun : string or function, optional. Default: ‘logcosh’

The functional form of the G function used in the approximation to neg-entropy. Could be either ‘logcosh’, ‘exp’, or ‘cube’. You can also provide your own function. It should return a tuple containing the value of the function, and of its derivative, in the point. Example:

def my_g(x):

  • return x ** 3, (3 * x ** 2).mean(axis=-1)
fun_args : dictionary, optional
Arguments to send to the functional form. If empty and if fun=’logcosh’, fun_args will take value {‘alpha’ : 1.0}.
max_iter : int, optional
Maximum number of iterations during fit.
tol : float, optional
Tolerance on update at each iteration.
w_init : None of an (n_components, n_components) ndarray
The mixing matrix to be used to initialize the algorithm.
random_state : int, RandomState instance or None, optional (default=None)
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.

Attributes

components_ : 2D array, shape (n_components, n_features)
The unmixing matrix.
mixing_ : array, shape (n_features, n_components)
The mixing matrix.
n_iter_ : int
If the algorithm is “deflation”, n_iter is the maximum number of iterations run across all components. Else they are just the number of iterations taken to converge.

Examples

>>> from sklearn.datasets import load_digits
>>> from sklearn.decomposition import FastICA
>>> X, _ = load_digits(return_X_y=True)
>>> transformer = FastICA(n_components=7,
...         random_state=0)
>>> X_transformed = transformer.fit_transform(X)
>>> X_transformed.shape
(1797, 7)

Notes

Implementation based on `A. Hyvarinen and E. Oja, Independent Component Analysis:

Algorithms and Applications, Neural Networks, 13(4-5), 2000, pp. 411-430`

Full API documentation: FastICAScikitsLearnNode

class mdp.nodes.RandomForestRegressorScikitsLearnNode

A random forest regressor. This node has been automatically generated by wrapping the sklearn.ensemble.forest.RandomForestRegressor class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. A random forest is a meta estimator that fits a number of classifying decision trees on various sub-samples of the dataset and uses averaging to improve the predictive accuracy and control over-fitting. The sub-sample size is always the same as the original input sample size but the samples are drawn with replacement if bootstrap=True (default).

Read more in the User Guide.

Parameters

n_estimators : integer, optional (default=10)

The number of trees in the forest.

Changed in version 0.20: The default value of n_estimators will change from 10 in version 0.20 to 100 in version 0.22.

criterion : string, optional (default=”mse”)

The function to measure the quality of a split. Supported criteria are “mse” for the mean squared error, which is equal to variance reduction as feature selection criterion, and “mae” for the mean absolute error.

New in version 0.18: Mean Absolute Error (MAE) criterion.

max_depth : integer or None, optional (default=None)
The maximum depth of the tree. If None, then nodes are expanded until all leaves are pure or until all leaves contain less than min_samples_split samples.
min_samples_split : int, float, optional (default=2)

The minimum number of samples required to split an internal node:

  • If int, then consider min_samples_split as the minimum number.
  • If float, then min_samples_split is a fraction and ceil(min_samples_split * n_samples) are the minimum number of samples for each split.

Changed in version 0.18: Added float values for fractions.

min_samples_leaf : int, float, optional (default=1)

The minimum number of samples required to be at a leaf node. A split point at any depth will only be considered if it leaves at least min_samples_leaf training samples in each of the left and right branches. This may have the effect of smoothing the model, especially in regression.

  • If int, then consider min_samples_leaf as the minimum number.
  • If float, then min_samples_leaf is a fraction and ceil(min_samples_leaf * n_samples) are the minimum number of samples for each node.

Changed in version 0.18: Added float values for fractions.

min_weight_fraction_leaf : float, optional (default=0.)
The minimum weighted fraction of the sum total of weights (of all the input samples) required to be at a leaf node. Samples have equal weight when sample_weight is not provided.
max_features : int, float, string or None, optional (default=”auto”)

The number of features to consider when looking for the best split:

  • If int, then consider max_features features at each split.
  • If float, then max_features is a fraction and int(max_features * n_features) features are considered at each split.
  • If “auto”, then max_features=n_features.
  • If “sqrt”, then max_features=sqrt(n_features).
  • If “log2”, then max_features=log2(n_features).
  • If None, then max_features=n_features.

Note: the search for a split does not stop until at least one valid partition of the node samples is found, even if it requires to effectively inspect more than max_features features.

max_leaf_nodes : int or None, optional (default=None)
Grow trees with max_leaf_nodes in best-first fashion. Best nodes are defined as relative reduction in impurity. If None then unlimited number of leaf nodes.
min_impurity_decrease : float, optional (default=0.)

A node will be split if this split induces a decrease of the impurity greater than or equal to this value.

The weighted impurity decrease equation is the following:

N_t / N * (impurity - N_t_R / N_t * right_impurity
                    - N_t_L / N_t * left_impurity)

where N is the total number of samples, N_t is the number of samples at the current node, N_t_L is the number of samples in the left child, and N_t_R is the number of samples in the right child.

N, N_t, N_t_R and N_t_L all refer to the weighted sum, if sample_weight is passed.

New in version 0.19.

min_impurity_split : float, (default=1e-7)

Threshold for early stopping in tree growth. A node will split if its impurity is above the threshold, otherwise it is a leaf.

Deprecated since version 0.19: min_impurity_split has been deprecated in favor of min_impurity_decrease in 0.19. The default value of min_impurity_split will change from 1e-7 to 0 in 0.23 and it will be removed in 0.25. Use min_impurity_decrease instead.

bootstrap : boolean, optional (default=True)
Whether bootstrap samples are used when building trees. If False, the whole datset is used to build each tree.
oob_score : bool, optional (default=False)
whether to use out-of-bag samples to estimate the R^2 on unseen data.
n_jobs : int or None, optional (default=None)
The number of jobs to run in parallel for both fit and predict. None` means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
random_state : int, RandomState instance or None, optional (default=None)
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.
verbose : int, optional (default=0)
Controls the verbosity when fitting and predicting.
warm_start : bool, optional (default=False)
When set to True, reuse the solution of the previous call to fit and add more estimators to the ensemble, otherwise, just fit a whole new forest. See the Glossary.

Attributes

estimators_ : list of DecisionTreeRegressor
The collection of fitted sub-estimators.
feature_importances_ : array of shape = [n_features]
The feature importances (the higher, the more important the feature).
n_features_ : int
The number of features when fit is performed.
n_outputs_ : int
The number of outputs when fit is performed.
oob_score_ : float
Score of the training dataset obtained using an out-of-bag estimate.
oob_prediction_ : array of shape = [n_samples]
Prediction computed with out-of-bag estimate on the training set.

Examples

>>> from sklearn.ensemble import RandomForestRegressor
>>> from sklearn.datasets import make_regression
>>> X, y = make_regression(n_features=4, n_informative=2,
...                        random_state=0, shuffle=False)
>>> regr = RandomForestRegressor(max_depth=2, random_state=0,
...                              n_estimators=100)
>>> regr.fit(X, y)
RandomForestRegressor(bootstrap=True, criterion='mse', max_depth=2,
           max_features='auto', max_leaf_nodes=None,
           min_impurity_decrease=0.0, min_impurity_split=None,
           min_samples_leaf=1, min_samples_split=2,
           min_weight_fraction_leaf=0.0, n_estimators=100, n_jobs=None,
           oob_score=False, random_state=0, verbose=0, warm_start=False)
>>> print(regr.feature_importances_)
[0.18146984 0.81473937 0.00145312 0.00233767]
>>> print(regr.predict([[0, 0, 0, 0]]))
[-8.32987858]

Notes

The default values for the parameters controlling the size of the trees (e.g. max_depth, min_samples_leaf, etc.) lead to fully grown and unpruned trees which can potentially be very large on some data sets. To reduce memory consumption, the complexity and size of the trees should be controlled by setting those parameter values.

The features are always randomly permuted at each split. Therefore, the best found split may vary, even with the same training data, max_features=n_features and bootstrap=False, if the improvement of the criterion is identical for several splits enumerated during the search of the best split. To obtain a deterministic behaviour during fitting, random_state has to be fixed.

The default value max_features="auto" uses n_features rather than n_features / 3. The latter was originally suggested in [1], whereas the former was more recently justified empirically in [2].

References

[1]
  1. Breiman, “Random Forests”, Machine Learning, 45(1), 5-32, 2001.
[2]P. Geurts, D. Ernst., and L. Wehenkel, “Extremely randomized trees”, Machine Learning, 63(1), 3-42, 2006.

See also

DecisionTreeRegressor, ExtraTreesRegressor

Full API documentation: RandomForestRegressorScikitsLearnNode

class mdp.nodes.MultinomialNBScikitsLearnNode

Naive Bayes classifier for multinomial models This node has been automatically generated by wrapping the sklearn.naive_bayes.MultinomialNB class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. The multinomial Naive Bayes classifier is suitable for classification with discrete features (e.g., word counts for text classification). The multinomial distribution normally requires integer feature counts. However, in practice, fractional counts such as tf-idf may also work.

Read more in the User Guide.

Parameters

alpha : float, optional (default=1.0)
Additive (Laplace/Lidstone) smoothing parameter (0 for no smoothing).
fit_prior : boolean, optional (default=True)
Whether to learn class prior probabilities or not. If false, a uniform prior will be used.
class_prior : array-like, size (n_classes,), optional (default=None)
Prior probabilities of the classes. If specified the priors are not adjusted according to the data.

Attributes

class_log_prior_ : array, shape (n_classes, )
Smoothed empirical log probability for each class.
intercept_ : array, shape (n_classes, )
Mirrors class_log_prior_ for interpreting MultinomialNB as a linear model.
feature_log_prob_ : array, shape (n_classes, n_features)
Empirical log probability of features given a class, P(x_i|y).
coef_ : array, shape (n_classes, n_features)
Mirrors feature_log_prob_ for interpreting MultinomialNB as a linear model.
class_count_ : array, shape (n_classes,)
Number of samples encountered for each class during fitting. This value is weighted by the sample weight when provided.
feature_count_ : array, shape (n_classes, n_features)
Number of samples encountered for each (class, feature) during fitting. This value is weighted by the sample weight when provided.

Examples

>>> import numpy as np
>>> X = np.random.randint(5, size=(6, 100))
>>> y = np.array([1, 2, 3, 4, 5, 6])
>>> from sklearn.naive_bayes import MultinomialNB
>>> clf = MultinomialNB()
>>> clf.fit(X, y)
MultinomialNB(alpha=1.0, class_prior=None, fit_prior=True)
>>> print(clf.predict(X[2:3]))
[3]

Notes

For the rationale behind the names coef_ and intercept_, i.e. naive Bayes as a linear classifier, see J. Rennie et al. (2003), Tackling the poor assumptions of naive Bayes text classifiers, ICML.

References

C.D. Manning, P. Raghavan and H. Schuetze (2008). Introduction to Information Retrieval. Cambridge University Press, pp. 234-265. http://nlp.stanford.edu/IR-book/html/htmledition/naive-bayes-text-classification-1.html

Full API documentation: MultinomialNBScikitsLearnNode

class mdp.nodes.LabelEncoderScikitsLearnNode

Encode labels with value between 0 and n_classes-1. This node has been automatically generated by wrapping the sklearn.preprocessing.label.LabelEncoder class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Read more in the User Guide.

Attributes

classes_ : array of shape (n_class,)
Holds the label for each class.

Examples

LabelEncoder can be used to normalize labels.

>>> from sklearn import preprocessing
>>> le = preprocessing.LabelEncoder()
>>> le.fit([1, 2, 2, 6])
LabelEncoder()
>>> le.classes_
array([1, 2, 6])
>>> le.transform([1, 1, 2, 6]) 
array([0, 0, 1, 2]...)
>>> le.inverse_transform([0, 0, 1, 2])
array([1, 1, 2, 6])

It can also be used to transform non-numerical labels (as long as they are hashable and comparable) to numerical labels.

>>> le = preprocessing.LabelEncoder()
>>> le.fit(["paris", "paris", "tokyo", "amsterdam"])
LabelEncoder()
>>> list(le.classes_)
['amsterdam', 'paris', 'tokyo']
>>> le.transform(["tokyo", "tokyo", "paris"]) 
array([2, 2, 1]...)
>>> list(le.inverse_transform([2, 2, 1]))
['tokyo', 'tokyo', 'paris']

See also

sklearn.preprocessing.OrdinalEncoder : encode categorical features
using a one-hot or ordinal encoding scheme.

Full API documentation: LabelEncoderScikitsLearnNode

class mdp.nodes.LocallyLinearEmbeddingScikitsLearnNode

Locally Linear Embedding This node has been automatically generated by wrapping the sklearn.manifold.locally_linear.LocallyLinearEmbedding class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Read more in the User Guide.

Parameters

n_neighbors : integer
number of neighbors to consider for each point.
n_components : integer
number of coordinates for the manifold
reg : float
regularization constant, multiplies the trace of the local covariance matrix of the distances.
eigen_solver : string, {‘auto’, ‘arpack’, ‘dense’}

auto : algorithm will attempt to choose the best method for input data

arpack : use arnoldi iteration in shift-invert mode.
For this method, M may be a dense matrix, sparse matrix, or general linear operator. Warning: ARPACK can be unstable for some problems. It is best to try several random seeds in order to check results.
dense : use standard dense matrix operations for the eigenvalue
decomposition. For this method, M must be an array or matrix type. This method should be avoided for large problems.
tol : float, optional
Tolerance for ‘arpack’ method Not used if eigen_solver==’dense’.
max_iter : integer
maximum number of iterations for the arpack solver. Not used if eigen_solver==’dense’.
method : string (‘standard’, ‘hessian’, ‘modified’ or ‘ltsa’)
standard : use the standard locally linear embedding algorithm. see
reference [1]
hessian : use the Hessian eigenmap method. This method requires
n_neighbors > n_components * (1 + (n_components + 1) / 2 see reference [2]
modified : use the modified locally linear embedding algorithm.
see reference [3]
ltsa : use local tangent space alignment algorithm
see reference [4]
hessian_tol : float, optional
Tolerance for Hessian eigenmapping method. Only used if method == 'hessian'
modified_tol : float, optional
Tolerance for modified LLE method. Only used if method == 'modified'
neighbors_algorithm : string [‘auto’|’brute’|’kd_tree’|’ball_tree’]
algorithm to use for nearest neighbors search, passed to neighbors.NearestNeighbors instance
random_state : int, RandomState instance or None, optional (default=None)
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random. Used when eigen_solver == ‘arpack’.
n_jobs : int or None, optional (default=None)
The number of parallel jobs to run. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.

Attributes

embedding_ : array-like, shape [n_samples, n_components]
Stores the embedding vectors
reconstruction_error_ : float
Reconstruction error associated with embedding_
nbrs_ : NearestNeighbors object
Stores nearest neighbors instance, including BallTree or KDtree if applicable.

Examples

>>> from sklearn.datasets import load_digits
>>> from sklearn.manifold import LocallyLinearEmbedding
>>> X, _ = load_digits(return_X_y=True)
>>> X.shape
(1797, 64)
>>> embedding = LocallyLinearEmbedding(n_components=2)
>>> X_transformed = embedding.fit_transform(X[:100])
>>> X_transformed.shape
(100, 2)

References

[1]Roweis, S. & Saul, L. Nonlinear dimensionality reduction by locally linear embedding. Science 290:2323 (2000).
[2]Donoho, D. & Grimes, C. Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data. Proc Natl Acad Sci U S A. 100:5591 (2003).
[3]Zhang, Z. & Wang, J. MLLE: Modified Locally Linear Embedding Using Multiple Weights. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.70.382
[4]Zhang, Z. & Zha, H. Principal manifolds and nonlinear dimensionality reduction via tangent space alignment. Journal of Shanghai Univ. 8:406 (2004)

Full API documentation: LocallyLinearEmbeddingScikitsLearnNode

class mdp.nodes.AdaBoostClassifierScikitsLearnNode

An AdaBoost classifier. This node has been automatically generated by wrapping the sklearn.ensemble.weight_boosting.AdaBoostClassifier class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. An AdaBoost [1] classifier is a meta-estimator that begins by fitting a classifier on the original dataset and then fits additional copies of the classifier on the same dataset but where the weights of incorrectly classified instances are adjusted such that subsequent classifiers focus more on difficult cases.

This class implements the algorithm known as AdaBoost-SAMME [2].

Read more in the User Guide.

Parameters

base_estimator : object, optional (default=None)
The base estimator from which the boosted ensemble is built. Support for sample weighting is required, as well as proper classes_ and n_classes_ attributes. If None, then the base estimator is DecisionTreeClassifier(max_depth=1)
n_estimators : integer, optional (default=50)
The maximum number of estimators at which boosting is terminated. In case of perfect fit, the learning procedure is stopped early.
learning_rate : float, optional (default=1.)
Learning rate shrinks the contribution of each classifier by learning_rate. There is a trade-off between learning_rate and n_estimators.
algorithm : {‘SAMME’, ‘SAMME.R’}, optional (default=’SAMME.R’)
If ‘SAMME.R’ then use the SAMME.R real boosting algorithm. base_estimator must support calculation of class probabilities. If ‘SAMME’ then use the SAMME discrete boosting algorithm. The SAMME.R algorithm typically converges faster than SAMME, achieving a lower test error with fewer boosting iterations.
random_state : int, RandomState instance or None, optional (default=None)
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.

Attributes

estimators_ : list of classifiers
The collection of fitted sub-estimators.
classes_ : array of shape = [n_classes]
The classes labels.
n_classes_ : int
The number of classes.
estimator_weights_ : array of floats
Weights for each estimator in the boosted ensemble.
estimator_errors_ : array of floats
Classification error for each estimator in the boosted ensemble.
feature_importances_ : array of shape = [n_features]
The feature importances if supported by the base_estimator.

See also

AdaBoostRegressor, GradientBoostingClassifier, sklearn.tree.DecisionTreeClassifier

References

[1]Y. Freund, R. Schapire, “A Decision-Theoretic Generalization of on-Line Learning and an Application to Boosting”, 1995.
[2]
  1. Zhu, H. Zou, S. Rosset, T. Hastie, “Multi-class AdaBoost”, 2009.

Full API documentation: AdaBoostClassifierScikitsLearnNode

class mdp.nodes.GaussianProcessClassifierScikitsLearnNode

Gaussian process classification (GPC) based on Laplace approximation. This node has been automatically generated by wrapping the sklearn.gaussian_process.gpc.GaussianProcessClassifier class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. The implementation is based on Algorithm 3.1, 3.2, and 5.1 of Gaussian Processes for Machine Learning (GPML) by Rasmussen and Williams.

Internally, the Laplace approximation is used for approximating the non-Gaussian posterior by a Gaussian.

Currently, the implementation is restricted to using the logistic link function. For multi-class classification, several binary one-versus rest classifiers are fitted. Note that this class thus does not implement a true multi-class Laplace approximation.

Parameters

kernel : kernel object
The kernel specifying the covariance function of the GP. If None is passed, the kernel “1.0 * RBF(1.0)” is used as default. Note that the kernel’s hyperparameters are optimized during fitting.
optimizer : string or callable, optional (default: “fmin_l_bfgs_b”)

Can either be one of the internally supported optimizers for optimizing the kernel’s parameters, specified by a string, or an externally defined optimizer passed as a callable. If a callable is passed, it must have the signature:

def optimizer(obj_func, initial_theta, bounds):

    - # * 'obj_func' is the objective function to be maximized, which
    - #   takes the hyperparameters theta as parameter and an
    - #   optional flag eval_gradient, which determines if the
    - #   gradient is returned additionally to the function value
    - # * 'initial_theta': the initial value for theta, which can be
    - #   used by local optimizers
    - # * 'bounds': the bounds on the values of theta
    - ....
    - # Returned are the best found hyperparameters theta and
    - # the corresponding value of the target function.
    - return theta_opt, func_min

Per default, the ‘fmin_l_bfgs_b’ algorithm from scipy.optimize is used. If None is passed, the kernel’s parameters are kept fixed. Available internal optimizers are:

'fmin_l_bfgs_b'
n_restarts_optimizer : int, optional (default: 0)
The number of restarts of the optimizer for finding the kernel’s parameters which maximize the log-marginal likelihood. The first run of the optimizer is performed from the kernel’s initial parameters, the remaining ones (if any) from thetas sampled log-uniform randomly from the space of allowed theta-values. If greater than 0, all bounds must be finite. Note that n_restarts_optimizer=0 implies that one run is performed.
max_iter_predict : int, optional (default: 100)
The maximum number of iterations in Newton’s method for approximating the posterior during predict. Smaller values will reduce computation time at the cost of worse results.
warm_start : bool, optional (default: False)
If warm-starts are enabled, the solution of the last Newton iteration on the Laplace approximation of the posterior mode is used as initialization for the next call of _posterior_mode(). This can speed up convergence when _posterior_mode is called several times on similar problems as in hyperparameter optimization. See the Glossary.
copy_X_train : bool, optional (default: True)
If True, a persistent copy of the training data is stored in the object. Otherwise, just a reference to the training data is stored, which might cause predictions to change if the data is modified externally.
random_state : int, RandomState instance or None, optional (default: None)
The generator used to initialize the centers. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.
multi_class : string, default : “one_vs_rest”
Specifies how multi-class classification problems are handled. Supported are “one_vs_rest” and “one_vs_one”. In “one_vs_rest”, one binary Gaussian process classifier is fitted for each class, which is trained to separate this class from the rest. In “one_vs_one”, one binary Gaussian process classifier is fitted for each pair of classes, which is trained to separate these two classes. The predictions of these binary predictors are combined into multi-class predictions. Note that “one_vs_one” does not support predicting probability estimates.
n_jobs : int or None, optional (default=None)
The number of jobs to use for the computation. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.

Attributes

kernel_ : kernel object
The kernel used for prediction. In case of binary classification, the structure of the kernel is the same as the one passed as parameter but with optimized hyperparameters. In case of multi-class classification, a CompoundKernel is returned which consists of the different kernels used in the one-versus-rest classifiers.
log_marginal_likelihood_value_ : float
The log-marginal-likelihood of self.kernel_.theta
classes_ : array-like, shape = (n_classes,)
Unique class labels.
n_classes_ : int
The number of classes in the training data

Examples

>>> from sklearn.datasets import load_iris
>>> from sklearn.gaussian_process import GaussianProcessClassifier
>>> from sklearn.gaussian_process.kernels import RBF
>>> X, y = load_iris(return_X_y=True)
>>> kernel = 1.0 * RBF(1.0)
>>> gpc = GaussianProcessClassifier(kernel=kernel,
...         random_state=0).fit(X, y)
>>> gpc.score(X, y) 
0.9866...
>>> gpc.predict_proba(X[:2,:])
array([[0.83548752, 0.03228706, 0.13222543],
       [0.79064206, 0.06525643, 0.14410151]])

New in version 0.18.

Full API documentation: GaussianProcessClassifierScikitsLearnNode

class mdp.nodes.LarsCVScikitsLearnNode

Cross-validated Least Angle Regression model. This node has been automatically generated by wrapping the sklearn.linear_model.least_angle.LarsCV class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. See glossary entry for cross-validation estimator.

Read more in the User Guide.

Parameters

fit_intercept : boolean
whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (e.g. data is expected to be already centered).
verbose : boolean or integer, optional
Sets the verbosity amount
max_iter : integer, optional
Maximum number of iterations to perform.
normalize : boolean, optional, default True
This parameter is ignored when fit_intercept is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use sklearn.preprocessing.StandardScaler before calling fit on an estimator with normalize=False.
precompute : True | False | ‘auto’ | array-like
Whether to use a precomputed Gram matrix to speed up calculations. If set to 'auto' let us decide. The Gram matrix cannot be passed as argument since we will use only subsets of X.
cv : int, cross-validation generator or an iterable, optional

Determines the cross-validation splitting strategy. Possible inputs for cv are:

  • None, to use the default 3-fold cross-validation,
  • integer, to specify the number of folds.
  • CV splitter,
  • An iterable yielding (train, test) splits as arrays of indices.

For integer/None inputs, KFold is used.

Refer User Guide for the various cross-validation strategies that can be used here.

Changed in version 0.20: cv default value if None will change from 3-fold to 5-fold in v0.22.

max_n_alphas : integer, optional
The maximum number of points on the path used to compute the residuals in the cross-validation
n_jobs : int or None, optional (default=None)
Number of CPUs to use during the cross validation. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
eps : float, optional
The machine-precision regularization in the computation of the Cholesky diagonal factors. Increase this for very ill-conditioned systems.
copy_X : boolean, optional, default True
If True, X will be copied; else, it may be overwritten.
positive : boolean (default=False)

Restrict coefficients to be >= 0. Be aware that you might want to remove fit_intercept which is set True by default.

Deprecated since version 0.20: The option is broken and deprecated. It will be removed in v0.22.

Attributes

coef_ : array, shape (n_features,)
parameter vector (w in the formulation formula)
intercept_ : float
independent term in decision function
coef_path_ : array, shape (n_features, n_alphas)
the varying values of the coefficients along the path
alpha_ : float
the estimated regularization parameter alpha
alphas_ : array, shape (n_alphas,)
the different values of alpha along the path
cv_alphas_ : array, shape (n_cv_alphas,)
all the values of alpha along the path for the different folds
mse_path_ : array, shape (n_folds, n_cv_alphas)
the mean square error on left-out for each fold along the path (alpha values given by cv_alphas)
n_iter_ : array-like or int
the number of iterations run by Lars with the optimal alpha.

Examples

>>> from sklearn.linear_model import LarsCV
>>> from sklearn.datasets import make_regression
>>> X, y = make_regression(n_samples=200, noise=4.0, random_state=0)
>>> reg = LarsCV(cv=5).fit(X, y)
>>> reg.score(X, y) 
0.9996...
>>> reg.alpha_
0.0254...
>>> reg.predict(X[:1,])
array([154.0842...])

See also

lars_path, LassoLars, LassoLarsCV

Full API documentation: LarsCVScikitsLearnNode

class mdp.nodes.AdditiveChi2SamplerScikitsLearnNode

Approximate feature map for additive chi2 kernel. This node has been automatically generated by wrapping the sklearn.kernel_approximation.AdditiveChi2Sampler class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Uses sampling the fourier transform of the kernel characteristic at regular intervals.

Since the kernel that is to be approximated is additive, the components of the input vectors can be treated separately. Each entry in the original space is transformed into 2*sample_steps+1 features, where sample_steps is a parameter of the method. Typical values of sample_steps include 1, 2 and 3.

Optimal choices for the sampling interval for certain data ranges can be computed (see the reference). The default values should be reasonable.

Read more in the User Guide.

Parameters

sample_steps : int, optional
Gives the number of (complex) sampling points.
sample_interval : float, optional
Sampling interval. Must be specified when sample_steps not in {1,2,3}.

Examples

>>> from sklearn.datasets import load_digits
>>> from sklearn.linear_model import SGDClassifier
>>> from sklearn.kernel_approximation import AdditiveChi2Sampler
>>> X, y = load_digits(return_X_y=True)
>>> chi2sampler = AdditiveChi2Sampler(sample_steps=2)
>>> X_transformed = chi2sampler.fit_transform(X, y)
>>> clf = SGDClassifier(max_iter=5, random_state=0, tol=1e-3)
>>> clf.fit(X_transformed, y)
SGDClassifier(alpha=0.0001, average=False, class_weight=None,
       early_stopping=False, epsilon=0.1, eta0=0.0, fit_intercept=True,
       l1_ratio=0.15, learning_rate='optimal', loss='hinge', max_iter=5,
       n_iter=None, n_iter_no_change=5, n_jobs=None, penalty='l2',
       power_t=0.5, random_state=0, shuffle=True, tol=0.001,
       validation_fraction=0.1, verbose=0, warm_start=False)
>>> clf.score(X_transformed, y) 
0.9543...

Notes

This estimator approximates a slightly different version of the additive chi squared kernel then metric.additive_chi2 computes.

See also

SkewedChi2Sampler : A Fourier-approximation to a non-additive variant of
the chi squared kernel.

sklearn.metrics.pairwise.chi2_kernel : The exact chi squared kernel.

sklearn.metrics.pairwise.additive_chi2_kernel : The exact additive chi
squared kernel.

References

See “Efficient additive kernels via explicit feature maps” A. Vedaldi and A. Zisserman, Pattern Analysis and Machine Intelligence, 2011

Full API documentation: AdditiveChi2SamplerScikitsLearnNode

class mdp.nodes.QuantileEstimatorScikitsLearnNode

An estimator predicting the alpha-quantile of the training targets. This node has been automatically generated by wrapping the sklearn.ensemble.gradient_boosting.QuantileEstimator class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Parameters

alpha : float
The quantile

Full API documentation: QuantileEstimatorScikitsLearnNode

class mdp.nodes.BirchScikitsLearnNode

Implements the Birch clustering algorithm. This node has been automatically generated by wrapping the sklearn.cluster.birch.Birch class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. It is a memory-efficient, online-learning algorithm provided as an alternative to MiniBatchKMeans. It constructs a tree data structure with the cluster centroids being read off the leaf. These can be either the final cluster centroids or can be provided as input to another clustering algorithm such as AgglomerativeClustering.

Read more in the User Guide.

Parameters

threshold : float, default 0.5
The radius of the subcluster obtained by merging a new sample and the closest subcluster should be lesser than the threshold. Otherwise a new subcluster is started. Setting this value to be very low promotes splitting and vice-versa.
branching_factor : int, default 50
Maximum number of CF subclusters in each node. If a new samples enters such that the number of subclusters exceed the branching_factor then that node is split into two nodes with the subclusters redistributed in each. The parent subcluster of that node is removed and two new subclusters are added as parents of the 2 split nodes.
n_clusters : int, instance of sklearn.cluster model, default 3

Number of clusters after the final clustering step, which treats the subclusters from the leaves as new samples.

  • None : the final clustering step is not performed and the subclusters are returned as they are.
  • sklearn.cluster Estimator : If a model is provided, the model is fit treating the subclusters as new samples and the initial data is mapped to the label of the closest subcluster.
  • int : the model fit is AgglomerativeClustering with n_clusters set to be equal to the int.
compute_labels : bool, default True
Whether or not to compute labels for each fit.
copy : bool, default True
Whether or not to make a copy of the given data. If set to False, the initial data will be overwritten.

Attributes

root_ : _CFNode
Root of the CFTree.
dummy_leaf_ : _CFNode
Start pointer to all the leaves.
subcluster_centers_ : ndarray,
Centroids of all subclusters read directly from the leaves.
subcluster_labels_ : ndarray,
Labels assigned to the centroids of the subclusters after they are clustered globally.
labels_ : ndarray, shape (n_samples,)
Array of labels assigned to the input data. if partial_fit is used instead of fit, they are assigned to the last batch of data.

Examples

>>> from sklearn.cluster import Birch
>>> X = [[0, 1], [0.3, 1], [-0.3, 1], [0, -1], [0.3, -1], [-0.3, -1]]
>>> brc = Birch(branching_factor=50, n_clusters=None, threshold=0.5,
... compute_labels=True)
>>> brc.fit(X) 
Birch(branching_factor=50, compute_labels=True, copy=True, n_clusters=None,
   threshold=0.5)
>>> brc.predict(X)
array([0, 0, 0, 1, 1, 1])

References

Notes

The tree data structure consists of nodes with each node consisting of a number of subclusters. The maximum number of subclusters in a node is determined by the branching factor. Each subcluster maintains a linear sum, squared sum and the number of samples in that subcluster. In addition, each subcluster can also have a node as its child, if the subcluster is not a member of a leaf node.

For a new point entering the root, it is merged with the subcluster closest to it and the linear sum, squared sum and the number of samples of that subcluster are updated. This is done recursively till the properties of the leaf node are updated.

Full API documentation: BirchScikitsLearnNode

class mdp.nodes.QuantileTransformerScikitsLearnNode

Transform features using quantiles information. This node has been automatically generated by wrapping the sklearn.preprocessing.data.QuantileTransformer class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. This method transforms the features to follow a uniform or a normal distribution. Therefore, for a given feature, this transformation tends to spread out the most frequent values. It also reduces the impact of (marginal) outliers: this is therefore a robust preprocessing scheme.

The transformation is applied on each feature independently. The cumulative distribution function of a feature is used to project the original values. Features values of new/unseen data that fall below or above the fitted range will be mapped to the bounds of the output distribution. Note that this transform is non-linear. It may distort linear correlations between variables measured at the same scale but renders variables measured at different scales more directly comparable.

Read more in the User Guide.

Parameters

n_quantiles : int, optional (default=1000)
Number of quantiles to be computed. It corresponds to the number of landmarks used to discretize the cumulative distribution function.
output_distribution : str, optional (default=’uniform’)
Marginal distribution for the transformed data. The choices are ‘uniform’ (default) or ‘normal’.
ignore_implicit_zeros : bool, optional (default=False)
Only applies to sparse matrices. If True, the sparse entries of the matrix are discarded to compute the quantile statistics. If False, these entries are treated as zeros.
subsample : int, optional (default=1e5)
Maximum number of samples used to estimate the quantiles for computational efficiency. Note that the subsampling procedure may differ for value-identical sparse and dense matrices.
random_state : int, RandomState instance or None, optional (default=None)
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random. Note that this is used by subsampling and smoothing noise.
copy : boolean, optional, (default=True)
Set to False to perform inplace transformation and avoid a copy (if the input is already a numpy array).

Attributes

quantiles_ : ndarray, shape (n_quantiles, n_features)
The values corresponding the quantiles of reference.
references_ : ndarray, shape(n_quantiles, )
Quantiles of references.

Examples

>>> import numpy as np
>>> from sklearn.preprocessing import QuantileTransformer
>>> rng = np.random.RandomState(0)
>>> X = np.sort(rng.normal(loc=0.5, scale=0.25, size=(25, 1)), axis=0)
>>> qt = QuantileTransformer(n_quantiles=10, random_state=0)
>>> qt.fit_transform(X) 
array([...])

See also

quantile_transform : Equivalent function without the estimator API. PowerTransformer : Perform mapping to a normal distribution using a power

transform.
StandardScaler : Perform standardization that is faster, but less robust
to outliers.
RobustScaler : Perform robust standardization that removes the influence
of outliers but does not put outliers and inliers on the same scale.

Notes

NaNs are treated as missing values: disregarded in fit, and maintained in transform.

For a comparison of the different scalers, transformers, and normalizers, see examples/preprocessing/plot_all_scaling.py.

Full API documentation: QuantileTransformerScikitsLearnNode

class mdp.nodes.CountVectorizerScikitsLearnNode

Convert a collection of text documents to a matrix of token counts This node has been automatically generated by wrapping the sklearn.feature_extraction.text.CountVectorizer class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. This implementation produces a sparse representation of the counts using scipy.sparse.csr_matrix.

If you do not provide an a-priori dictionary and you do not use an analyzer that does some kind of feature selection then the number of features will be equal to the vocabulary size found by analyzing the data.

Read more in the User Guide.

Parameters

input : string {‘filename’, ‘file’, ‘content’}

If ‘filename’, the sequence passed as an argument to fit is expected to be a list of filenames that need reading to fetch the raw content to analyze.

If ‘file’, the sequence items must have a ‘read’ method (file-like object) that is called to fetch the bytes in memory.

Otherwise the input is expected to be the sequence strings or bytes items are expected to be analyzed directly.

encoding : string, ‘utf-8’ by default.
If bytes or files are given to analyze, this encoding is used to decode.
decode_error : {‘strict’, ‘ignore’, ‘replace’}
Instruction on what to do if a byte sequence is given to analyze that contains characters not of the given encoding. By default, it is ‘strict’, meaning that a UnicodeDecodeError will be raised. Other values are ‘ignore’ and ‘replace’.
strip_accents : {‘ascii’, ‘unicode’, None}

Remove accents and perform other character normalization during the preprocessing step. ‘ascii’ is a fast method that only works on characters that have an direct ASCII mapping. ‘unicode’ is a slightly slower method that works on any characters. None (default) does nothing.

Both ‘ascii’ and ‘unicode’ use NFKD normalization from unicodedata.normalize().

lowercase : boolean, True by default
Convert all characters to lowercase before tokenizing.
preprocessor : callable or None (default)
Override the preprocessing (string transformation) stage while preserving the tokenizing and n-grams generation steps.
tokenizer : callable or None (default)
Override the string tokenization step while preserving the preprocessing and n-grams generation steps. Only applies if analyzer == 'word'.
stop_words : string {‘english’}, list, or None (default)

If ‘english’, a built-in stop word list for English is used. There are several known issues with ‘english’ and you should consider an alternative (see stop_words).

If a list, that list is assumed to contain stop words, all of which will be removed from the resulting tokens. Only applies if analyzer == 'word'.

If None, no stop words will be used. max_df can be set to a value in the range [0.7, 1.0) to automatically detect and filter stop words based on intra corpus document frequency of terms.

token_pattern : string
Regular expression denoting what constitutes a “token”, only used if analyzer == 'word'. The default regexp select tokens of 2 or more alphanumeric characters (punctuation is completely ignored and always treated as a token separator).
ngram_range : tuple (min_n, max_n)
The lower and upper boundary of the range of n-values for different n-grams to be extracted. All values of n such that min_n <= n <= max_n will be used.
analyzer : string, {‘word’, ‘char’, ‘char_wb’} or callable

Whether the feature should be made of word or character n-grams. Option ‘char_wb’ creates character n-grams only from text inside word boundaries; n-grams at the edges of words are padded with space.

If a callable is passed it is used to extract the sequence of features out of the raw, unprocessed input.

max_df : float in range [0.0, 1.0] or int, default=1.0
When building the vocabulary ignore terms that have a document frequency strictly higher than the given threshold (corpus-specific stop words). If float, the parameter represents a proportion of documents, integer absolute counts. This parameter is ignored if vocabulary is not None.
min_df : float in range [0.0, 1.0] or int, default=1
When building the vocabulary ignore terms that have a document frequency strictly lower than the given threshold. This value is also called cut-off in the literature. If float, the parameter represents a proportion of documents, integer absolute counts. This parameter is ignored if vocabulary is not None.
max_features : int or None, default=None

If not None, build a vocabulary that only consider the top max_features ordered by term frequency across the corpus.

This parameter is ignored if vocabulary is not None.

vocabulary : Mapping or iterable, optional
Either a Mapping (e.g., a dict) where keys are terms and values are indices in the feature matrix, or an iterable over terms. If not given, a vocabulary is determined from the input documents. Indices in the mapping should not be repeated and should not have any gap between 0 and the largest index.
binary : boolean, default=False
If True, all non zero counts are set to 1. This is useful for discrete probabilistic models that model binary events rather than integer counts.
dtype : type, optional
Type of the matrix returned by fit_transform() or transform().

Attributes

vocabulary_ : dict
A mapping of terms to feature indices.
stop_words_ : set

Terms that were ignored because they either:

  • occurred in too many documents (max_df)
  • occurred in too few documents (min_df)
  • were cut off by feature selection (max_features).

This is only available if no vocabulary was given.

Examples

>>> from sklearn.feature_extraction.text import CountVectorizer
>>> corpus = [
...     'This is the first document.',
...     'This document is the second document.',
...     'And this is the third one.',
...     'Is this the first document?',
... ]
>>> vectorizer = CountVectorizer()
>>> X = vectorizer.fit_transform(corpus)
>>> print(vectorizer.get_feature_names())
['and', 'document', 'first', 'is', 'one', 'second', 'the', 'third', 'this']
>>> print(X.toarray())  
[[0 1 1 1 0 0 1 0 1]
 [0 2 0 1 0 1 1 0 1]
 [1 0 0 1 1 0 1 1 1]
 [0 1 1 1 0 0 1 0 1]]

See also

HashingVectorizer, TfidfVectorizer

Notes

The stop_words_ attribute can get large and increase the model size when pickling. This attribute is provided only for introspection and can be safely removed using delattr or set to None before pickling.

Full API documentation: CountVectorizerScikitsLearnNode

class mdp.nodes.ExtraTreesRegressorScikitsLearnNode

An extra-trees regressor. This node has been automatically generated by wrapping the sklearn.ensemble.forest.ExtraTreesRegressor class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. This class implements a meta estimator that fits a number of randomized decision trees (a.k.a. extra-trees) on various sub-samples of the dataset and uses averaging to improve the predictive accuracy and control over-fitting.

Read more in the User Guide.

Parameters

n_estimators : integer, optional (default=10)

The number of trees in the forest.

Changed in version 0.20: The default value of n_estimators will change from 10 in version 0.20 to 100 in version 0.22.

criterion : string, optional (default=”mse”)

The function to measure the quality of a split. Supported criteria are “mse” for the mean squared error, which is equal to variance reduction as feature selection criterion, and “mae” for the mean absolute error.

New in version 0.18: Mean Absolute Error (MAE) criterion.

max_depth : integer or None, optional (default=None)
The maximum depth of the tree. If None, then nodes are expanded until all leaves are pure or until all leaves contain less than min_samples_split samples.
min_samples_split : int, float, optional (default=2)

The minimum number of samples required to split an internal node:

  • If int, then consider min_samples_split as the minimum number.
  • If float, then min_samples_split is a fraction and ceil(min_samples_split * n_samples) are the minimum number of samples for each split.

Changed in version 0.18: Added float values for fractions.

min_samples_leaf : int, float, optional (default=1)

The minimum number of samples required to be at a leaf node. A split point at any depth will only be considered if it leaves at least min_samples_leaf training samples in each of the left and right branches. This may have the effect of smoothing the model, especially in regression.

  • If int, then consider min_samples_leaf as the minimum number.
  • If float, then min_samples_leaf is a fraction and ceil(min_samples_leaf * n_samples) are the minimum number of samples for each node.

Changed in version 0.18: Added float values for fractions.

min_weight_fraction_leaf : float, optional (default=0.)
The minimum weighted fraction of the sum total of weights (of all the input samples) required to be at a leaf node. Samples have equal weight when sample_weight is not provided.
max_features : int, float, string or None, optional (default=”auto”)

The number of features to consider when looking for the best split:

  • If int, then consider max_features features at each split.
  • If float, then max_features is a fraction and int(max_features * n_features) features are considered at each split.
  • If “auto”, then max_features=n_features.
  • If “sqrt”, then max_features=sqrt(n_features).
  • If “log2”, then max_features=log2(n_features).
  • If None, then max_features=n_features.

Note: the search for a split does not stop until at least one valid partition of the node samples is found, even if it requires to effectively inspect more than max_features features.

max_leaf_nodes : int or None, optional (default=None)
Grow trees with max_leaf_nodes in best-first fashion. Best nodes are defined as relative reduction in impurity. If None then unlimited number of leaf nodes.
min_impurity_decrease : float, optional (default=0.)

A node will be split if this split induces a decrease of the impurity greater than or equal to this value.

The weighted impurity decrease equation is the following:

N_t / N * (impurity - N_t_R / N_t * right_impurity
                    - N_t_L / N_t * left_impurity)

where N is the total number of samples, N_t is the number of samples at the current node, N_t_L is the number of samples in the left child, and N_t_R is the number of samples in the right child.

N, N_t, N_t_R and N_t_L all refer to the weighted sum, if sample_weight is passed.

New in version 0.19.

min_impurity_split : float, (default=1e-7)

Threshold for early stopping in tree growth. A node will split if its impurity is above the threshold, otherwise it is a leaf.

Deprecated since version 0.19: min_impurity_split has been deprecated in favor of min_impurity_decrease in 0.19. The default value of min_impurity_split will change from 1e-7 to 0 in 0.23 and it will be removed in 0.25. Use min_impurity_decrease instead.

bootstrap : boolean, optional (default=False)
Whether bootstrap samples are used when building trees. If False, the whole datset is used to build each tree.
oob_score : bool, optional (default=False)
Whether to use out-of-bag samples to estimate the R^2 on unseen data.
n_jobs : int or None, optional (default=None)
The number of jobs to run in parallel for both fit and predict. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
random_state : int, RandomState instance or None, optional (default=None)
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.
verbose : int, optional (default=0)
Controls the verbosity when fitting and predicting.
warm_start : bool, optional (default=False)
When set to True, reuse the solution of the previous call to fit and add more estimators to the ensemble, otherwise, just fit a whole new forest. See the Glossary.

Attributes

estimators_ : list of DecisionTreeRegressor
The collection of fitted sub-estimators.
feature_importances_ : array of shape = [n_features]
The feature importances (the higher, the more important the feature).
n_features_ : int
The number of features.
n_outputs_ : int
The number of outputs.
oob_score_ : float
Score of the training dataset obtained using an out-of-bag estimate.
oob_prediction_ : array of shape = [n_samples]
Prediction computed with out-of-bag estimate on the training set.

Notes

The default values for the parameters controlling the size of the trees (e.g. max_depth, min_samples_leaf, etc.) lead to fully grown and unpruned trees which can potentially be very large on some data sets. To reduce memory consumption, the complexity and size of the trees should be controlled by setting those parameter values.

References

[1]P. Geurts, D. Ernst., and L. Wehenkel, “Extremely randomized trees”, Machine Learning, 63(1), 3-42, 2006.

See also

sklearn.tree.ExtraTreeRegressor: Base estimator for this ensemble. RandomForestRegressor: Ensemble regressor using trees with optimal splits.

Full API documentation: ExtraTreesRegressorScikitsLearnNode

class mdp.nodes.LabelPropagationScikitsLearnNode

Label Propagation classifier This node has been automatically generated by wrapping the sklearn.semi_supervised.label_propagation.LabelPropagation class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Read more in the User Guide.

Parameters

kernel : {‘knn’, ‘rbf’, callable}
String identifier for kernel function to use or the kernel function itself. Only ‘rbf’ and ‘knn’ strings are valid inputs. The function passed should take two inputs, each of shape [n_samples, n_features], and return a [n_samples, n_samples] shaped weight matrix.
gamma : float
Parameter for rbf kernel
n_neighbors : integer > 0
Parameter for knn kernel
alpha : float

Clamping factor.

Deprecated since version 0.19: This parameter will be removed in 0.21. ‘alpha’ is fixed to zero in ‘LabelPropagation’.

max_iter : integer
Change maximum number of iterations allowed
tol : float
Convergence tolerance: threshold to consider the system at steady state
n_jobs : int or None, optional (default=None)
The number of parallel jobs to run. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.

Attributes

X_ : array, shape = [n_samples, n_features]
Input array.
classes_ : array, shape = [n_classes]
The distinct labels used in classifying instances.
label_distributions_ : array, shape = [n_samples, n_classes]
Categorical distribution for each item.
transduction_ : array, shape = [n_samples]
Label assigned to each item via the transduction.
n_iter_ : int
Number of iterations run.

Examples

>>> import numpy as np
>>> from sklearn import datasets
>>> from sklearn.semi_supervised import LabelPropagation
>>> label_prop_model = LabelPropagation()
>>> iris = datasets.load_iris()
>>> rng = np.random.RandomState(42)
>>> random_unlabeled_points = rng.rand(len(iris.target)) < 0.3
>>> labels = np.copy(iris.target)
>>> labels[random_unlabeled_points] = -1
>>> label_prop_model.fit(iris.data, labels)
... 
LabelPropagation(...)

References

Xiaojin Zhu and Zoubin Ghahramani. Learning from labeled and unlabeled data with label propagation. Technical Report CMU-CALD-02-107, Carnegie Mellon University, 2002 http://pages.cs.wisc.edu/~jerryzhu/pub/CMU-CALD-02-107.pdf

See Also

LabelSpreading : Alternate label propagation strategy more robust to noise

Full API documentation: LabelPropagationScikitsLearnNode

class mdp.nodes.GaussianMixtureScikitsLearnNode

Gaussian Mixture. This node has been automatically generated by wrapping the sklearn.mixture.gaussian_mixture.GaussianMixture class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Representation of a Gaussian mixture model probability distribution. This class allows to estimate the parameters of a Gaussian mixture distribution.

Read more in the User Guide.

New in version 0.18.

Parameters

n_components : int, defaults to 1.
The number of mixture components.
covariance_type : {‘full’ (default), ‘tied’, ‘diag’, ‘spherical’}

String describing the type of covariance parameters to use. Must be one of:

‘full’
each component has its own general covariance matrix
‘tied’
all components share the same general covariance matrix
‘diag’
each component has its own diagonal covariance matrix
‘spherical’
each component has its own single variance
tol : float, defaults to 1e-3.
The convergence threshold. EM iterations will stop when the lower bound average gain is below this threshold.
reg_covar : float, defaults to 1e-6.
Non-negative regularization added to the diagonal of covariance. Allows to assure that the covariance matrices are all positive.
max_iter : int, defaults to 100.
The number of EM iterations to perform.
n_init : int, defaults to 1.
The number of initializations to perform. The best results are kept.
init_params : {‘kmeans’, ‘random’}, defaults to ‘kmeans’.

The method used to initialize the weights, the means and the precisions. Must be one of:

'kmeans' : responsibilities are initialized using kmeans.
'random' : responsibilities are initialized randomly.
weights_init : array-like, shape (n_components, ), optional
The user-provided initial weights, defaults to None. If it None, weights are initialized using the init_params method.
means_init : array-like, shape (n_components, n_features), optional
The user-provided initial means, defaults to None, If it None, means are initialized using the init_params method.
precisions_init : array-like, optional.

The user-provided initial precisions (inverse of the covariance matrices), defaults to None. If it None, precisions are initialized using the ‘init_params’ method. The shape depends on ‘covariance_type’:

(n_components,)                        if 'spherical',
(n_features, n_features)               if 'tied',
(n_components, n_features)             if 'diag',
(n_components, n_features, n_features) if 'full'
random_state : int, RandomState instance or None, optional (default=None)
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.
warm_start : bool, default to False.
If ‘warm_start’ is True, the solution of the last fitting is used as initialization for the next call of fit(). This can speed up convergence when fit is called several times on similar problems. In that case, ‘n_init’ is ignored and only a single initialization occurs upon the first call. See the Glossary.
verbose : int, default to 0.
Enable verbose output. If 1 then it prints the current initialization and each iteration step. If greater than 1 then it prints also the log probability and the time needed for each step.
verbose_interval : int, default to 10.
Number of iteration done before the next print.

Attributes

weights_ : array-like, shape (n_components,)
The weights of each mixture components.
means_ : array-like, shape (n_components, n_features)
The mean of each mixture component.
covariances_ : array-like

The covariance of each mixture component. The shape depends on covariance_type:

(n_components,)                        if 'spherical',
(n_features, n_features)               if 'tied',
(n_components, n_features)             if 'diag',
(n_components, n_features, n_features) if 'full'
precisions_ : array-like

The precision matrices for each component in the mixture. A precision matrix is the inverse of a covariance matrix. A covariance matrix is symmetric positive definite so the mixture of Gaussian can be equivalently parameterized by the precision matrices. Storing the precision matrices instead of the covariance matrices makes it more efficient to compute the log-likelihood of new samples at test time. The shape depends on covariance_type:

(n_components,)                        if 'spherical',
(n_features, n_features)               if 'tied',
(n_components, n_features)             if 'diag',
(n_components, n_features, n_features) if 'full'
precisions_cholesky_ : array-like

The cholesky decomposition of the precision matrices of each mixture component. A precision matrix is the inverse of a covariance matrix. A covariance matrix is symmetric positive definite so the mixture of Gaussian can be equivalently parameterized by the precision matrices. Storing the precision matrices instead of the covariance matrices makes it more efficient to compute the log-likelihood of new samples at test time. The shape depends on covariance_type:

(n_components,)                        if 'spherical',
(n_features, n_features)               if 'tied',
(n_components, n_features)             if 'diag',
(n_components, n_features, n_features) if 'full'
converged_ : bool
True when convergence was reached in fit(), False otherwise.
n_iter_ : int
Number of step used by the best fit of EM to reach the convergence.
lower_bound_ : float
Lower bound value on the log-likelihood (of the training data with respect to the model) of the best fit of EM.

See Also

BayesianGaussianMixture : Gaussian mixture model fit with a variational
inference.

Full API documentation: GaussianMixtureScikitsLearnNode

class mdp.nodes.MeanEstimatorScikitsLearnNode

This node has been automatically generated by wrapping the sklearn.ensemble.gradient_boosting.MeanEstimator class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute.

Full API documentation: MeanEstimatorScikitsLearnNode

class mdp.nodes.SelectFromModelScikitsLearnNode

Meta-transformer for selecting features based on importance weights. This node has been automatically generated by wrapping the sklearn.feature_selection.from_model.SelectFromModel class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. .. versionadded:: 0.17

Parameters

estimator : object
The base estimator from which the transformer is built. This can be both a fitted (if prefit is set to True) or a non-fitted estimator. The estimator must have either a feature_importances_ or coef_ attribute after fitting.
threshold : string, float, optional default None
The threshold value to use for feature selection. Features whose importance is greater or equal are kept while the others are discarded. If “median” (resp. “mean”), then the threshold value is the median (resp. the mean) of the feature importances. A scaling factor (e.g., “1.25*mean”) may also be used. If None and if the estimator has a parameter penalty set to l1, either explicitly or implicitly (e.g, Lasso), the threshold used is 1e-5. Otherwise, “mean” is used by default.
prefit : bool, default False
Whether a prefit model is expected to be passed into the constructor directly or not. If True, transform must be called directly and SelectFromModel cannot be used with cross_val_score, GridSearchCV and similar utilities that clone the estimator. Otherwise train the model using fit and then transform to do feature selection.
norm_order : non-zero int, inf, -inf, default 1
Order of the norm used to filter the vectors of coefficients below threshold in the case where the coef_ attribute of the estimator is of dimension 2.
max_features : int or None, optional

The maximum number of features selected scoring above threshold. To disable threshold and only select based on max_features, set threshold=-np.inf.

New in version 0.20.

Attributes

estimator_ : an estimator
The base estimator from which the transformer is built. This is stored only when a non-fitted estimator is passed to the SelectFromModel, i.e when prefit is False.
threshold_ : float
The threshold value used for feature selection.

Full API documentation: SelectFromModelScikitsLearnNode

class mdp.nodes.RadiusNeighborsRegressorScikitsLearnNode

Regression based on neighbors within a fixed radius. This node has been automatically generated by wrapping the sklearn.neighbors.regression.RadiusNeighborsRegressor class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. The target is predicted by local interpolation of the targets associated of the nearest neighbors in the training set.

Read more in the User Guide.

Parameters

radius : float, optional (default = 1.0)
Range of parameter space to use by default for radius_neighbors() queries.
weights : str or callable

weight function used in prediction. Possible values:

  • ‘uniform’ : uniform weights. All points in each neighborhood are weighted equally.
  • ‘distance’ : weight points by the inverse of their distance. in this case, closer neighbors of a query point will have a greater influence than neighbors which are further away.
  • [callable] : a user-defined function which accepts an array of distances, and returns an array of the same shape containing the weights.

Uniform weights are used by default.

algorithm : {‘auto’, ‘ball_tree’, ‘kd_tree’, ‘brute’}, optional

Algorithm used to compute the nearest neighbors:

  • ‘ball_tree’ will use BallTree
  • ‘kd_tree’ will use KDTree
  • ‘brute’ will use a brute-force search.
  • ‘auto’ will attempt to decide the most appropriate algorithm based on the values passed to fit() method.

Note: fitting on sparse input will override the setting of this parameter, using brute force.

leaf_size : int, optional (default = 30)
Leaf size passed to BallTree or KDTree. This can affect the speed of the construction and query, as well as the memory required to store the tree. The optimal value depends on the nature of the problem.
p : integer, optional (default = 2)
Power parameter for the Minkowski metric. When p = 1, this is equivalent to using manhattan_distance (l1), and euclidean_distance (l2) for p = 2. For arbitrary p, minkowski_distance (l_p) is used.
metric : string or callable, default ‘minkowski’
the distance metric to use for the tree. The default metric is minkowski, and with p=2 is equivalent to the standard Euclidean metric. See the documentation of the DistanceMetric class for a list of available metrics.
metric_params : dict, optional (default = None)
Additional keyword arguments for the metric function.
n_jobs : int or None, optional (default=None)
The number of parallel jobs to run for neighbors search.
None means 1 unless in a joblib.parallel_backend context.

-1 means using all processors. See Glossary for more details.

Examples

>>> X = [[0], [1], [2], [3]]
>>> y = [0, 0, 1, 1]
>>> from sklearn.neighbors import RadiusNeighborsRegressor
>>> neigh = RadiusNeighborsRegressor(radius=1.0)
>>> neigh.fit(X, y) 
RadiusNeighborsRegressor(...)
>>> print(neigh.predict([[1.5]]))
[0.5]

See also

NearestNeighbors KNeighborsRegressor KNeighborsClassifier RadiusNeighborsClassifier

Notes

See Nearest Neighbors in the online documentation for a discussion of the choice of algorithm and leaf_size.

https://en.wikipedia.org/wiki/K-nearest_neighbor_algorithm

Full API documentation: RadiusNeighborsRegressorScikitsLearnNode

class mdp.nodes.PLSSVDScikitsLearnNode

Partial Least Square SVD This node has been automatically generated by wrapping the sklearn.cross_decomposition.pls_.PLSSVD class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Simply perform a svd on the crosscovariance matrix: X’Y There are no iterative deflation here.

Read more in the User Guide.

Parameters

n_components : int, default 2
Number of components to keep.
scale : boolean, default True
Whether to scale X and Y.
copy : boolean, default True
Whether to copy X and Y, or perform in-place computations.

Attributes

x_weights_ : array, [p, n_components]
X block weights vectors.
y_weights_ : array, [q, n_components]
Y block weights vectors.
x_scores_ : array, [n_samples, n_components]
X scores.
y_scores_ : array, [n_samples, n_components]
Y scores.

Examples

>>> import numpy as np
>>> from sklearn.cross_decomposition import PLSSVD
>>> X = np.array([[0., 0., 1.],
...     [1.,0.,0.],
...     [2.,2.,2.],
...     [2.,5.,4.]])
>>> Y = np.array([[0.1, -0.2],
...     [0.9, 1.1],
...     [6.2, 5.9],
...     [11.9, 12.3]])
>>> plsca = PLSSVD(n_components=2)
>>> plsca.fit(X, Y)
PLSSVD(copy=True, n_components=2, scale=True)
>>> X_c, Y_c = plsca.transform(X, Y)
>>> X_c.shape, Y_c.shape
((4, 2), (4, 2))

See also

PLSCanonical CCA

Full API documentation: PLSSVDScikitsLearnNode

class mdp.nodes.GaussianRandomProjectionScikitsLearnNode

Reduce dimensionality through Gaussian random projection This node has been automatically generated by wrapping the sklearn.random_projection.GaussianRandomProjection class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. The components of the random matrix are drawn from N(0, 1 / n_components).

Read more in the User Guide.

Parameters

n_components : int or ‘auto’, optional (default = ‘auto’)

Dimensionality of the target projection space.

n_components can be automatically adjusted according to the number of samples in the dataset and the bound given by the Johnson-Lindenstrauss lemma. In that case the quality of the embedding is controlled by the eps parameter.

It should be noted that Johnson-Lindenstrauss lemma can yield very conservative estimated of the required number of components as it makes no assumption on the structure of the dataset.

eps : strictly positive float, optional (default=0.1)

Parameter to control the quality of the embedding according to the Johnson-Lindenstrauss lemma when n_components is set to ‘auto’.

Smaller values lead to better embedding and higher number of dimensions (n_components) in the target projection space.

random_state : int, RandomState instance or None, optional (default=None)
Control the pseudo random number generator used to generate the matrix at fit time. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.

Attributes

n_component_ : int
Concrete number of components computed when n_components=”auto”.
components_ : numpy array of shape [n_components, n_features]
Random matrix used for the projection.

Examples

>>> import numpy as np
>>> from sklearn.random_projection import GaussianRandomProjection
>>> X = np.random.rand(100, 10000)
>>> transformer = GaussianRandomProjection()
>>> X_new = transformer.fit_transform(X)
>>> X_new.shape
(100, 3947)

See Also

SparseRandomProjection

Full API documentation: GaussianRandomProjectionScikitsLearnNode

class mdp.nodes.OneHotEncoderScikitsLearnNode

Encode categorical integer features as a one-hot numeric array. This node has been automatically generated by wrapping the sklearn.preprocessing._encoders.OneHotEncoder class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. The input to this transformer should be an array-like of integers or strings, denoting the values taken on by categorical (discrete) features. The features are encoded using a one-hot (aka ‘one-of-K’ or ‘dummy’) encoding scheme. This creates a binary column for each category and returns a sparse matrix or dense array.

By default, the encoder derives the categories based on the unique values in each feature. Alternatively, you can also specify the categories manually. The OneHotEncoder previously assumed that the input features take on values in the range [0, max(values)). This behaviour is deprecated.

This encoding is needed for feeding categorical data to many scikit-learn estimators, notably linear models and SVMs with the standard kernels.

Note: a one-hot encoding of y labels should use a LabelBinarizer instead.

Read more in the User Guide.

Parameters

categories : ‘auto’ or a list of lists/arrays of values, default=’auto’.

Categories (unique values) per feature:

  • ‘auto’ : Determine categories automatically from the training data.
  • list : categories[i] holds the categories expected in the ith column. The passed categories should not mix strings and numeric values within a single feature, and should be sorted in case of numeric values.

The used categories can be found in the categories_ attribute.

sparse : boolean, default=True
Will return sparse matrix if set True else will return an array.
dtype : number type, default=np.float
Desired dtype of output.
handle_unknown : ‘error’ or ‘ignore’, default=’error’.
Whether to raise an error or ignore if an unknown categorical feature is present during transform (default is to raise). When this parameter is set to ‘ignore’ and an unknown category is encountered during transform, the resulting one-hot encoded columns for this feature will be all zeros. In the inverse transform, an unknown category will be denoted as None.
n_values : ‘auto’, int or array of ints, default=’auto’

Number of values per feature.

  • ‘auto’ : determine value range from training data.

  • int : number of categorical values per feature.

    Each feature value should be in range(n_values)

  • array : n_values[i] is the number of categorical values in

    X[:, i]. Each feature value should be in range(n_values[i])

Deprecated since version 0.20: The n_values keyword was deprecated in version 0.20 and will be removed in 0.22. Use categories instead.

categorical_features : ‘all’ or array of indices or mask, default=’all’

Specify what features are treated as categorical.

  • ‘all’: All features are treated as categorical.
  • array of indices: Array of categorical feature indices.
  • mask: Array of length n_features and with dtype=bool.

Non-categorical features are always stacked to the right of the matrix.

Deprecated since version 0.20: The categorical_features keyword was deprecated in version 0.20 and will be removed in 0.22. You can use the ColumnTransformer instead.

Attributes

categories_ : list of arrays
The categories of each feature determined during fitting (in order of the features in X and corresponding with the output of transform).
active_features_ : array

Indices for active features, meaning values that actually occur in the training set. Only available when n_values is 'auto'.

Deprecated since version 0.20: The active_features_ attribute was deprecated in version 0.20 and will be removed in 0.22.

feature_indices_ : array of shape (n_features,)

Indices to feature ranges. Feature i in the original data is mapped to features from feature_indices_[i] to feature_indices_[i+1] (and then potentially masked by active_features_ afterwards)

Deprecated since version 0.20: The feature_indices_ attribute was deprecated in version 0.20 and will be removed in 0.22.

n_values_ : array of shape (n_features,)

Maximum number of values per feature.

Deprecated since version 0.20: The n_values_ attribute was deprecated in version 0.20 and will be removed in 0.22.

Examples

Given a dataset with two features, we let the encoder find the unique values per feature and transform the data to a binary one-hot encoding.

>>> from sklearn.preprocessing import OneHotEncoder
>>> enc = OneHotEncoder(handle_unknown='ignore')
>>> X = [['Male', 1], ['Female', 3], ['Female', 2]]
>>> enc.fit(X)
... 
OneHotEncoder(categorical_features=None, categories=None,
       dtype=<... 'numpy.float64'>, handle_unknown='ignore',
       n_values=None, sparse=True)
>>> enc.categories_
[array(['Female', 'Male'], dtype=object), array([1, 2, 3], dtype=object)]
>>> enc.transform([['Female', 1], ['Male', 4]]).toarray()
array([[1., 0., 1., 0., 0.],
       [0., 1., 0., 0., 0.]])
>>> enc.inverse_transform([[0, 1, 1, 0, 0], [0, 0, 0, 1, 0]])
array([['Male', 1],
       [None, 2]], dtype=object)
>>> enc.get_feature_names()
array(['x0_Female', 'x0_Male', 'x1_1', 'x1_2', 'x1_3'], dtype=object)

See also

sklearn.preprocessing.OrdinalEncoder : performs an ordinal (integer)
encoding of the categorical features.
sklearn.feature_extraction.DictVectorizer : performs a one-hot encoding of
dictionary items (also handles string-valued features).
sklearn.feature_extraction.FeatureHasher : performs an approximate one-hot
encoding of dictionary items or strings.
sklearn.preprocessing.LabelBinarizer : binarizes labels in a one-vs-all
fashion.
sklearn.preprocessing.MultiLabelBinarizer : transforms between iterable of
iterables and a multilabel format, e.g. a (samples x classes) binary matrix indicating the presence of a class label.

Full API documentation: OneHotEncoderScikitsLearnNode

class mdp.nodes.KNeighborsRegressorScikitsLearnNode

Regression based on k-nearest neighbors. This node has been automatically generated by wrapping the sklearn.neighbors.regression.KNeighborsRegressor class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. The target is predicted by local interpolation of the targets associated of the nearest neighbors in the training set.

Read more in the User Guide.

Parameters

n_neighbors : int, optional (default = 5)
Number of neighbors to use by default for kneighbors() queries.
weights : str or callable

weight function used in prediction. Possible values:

  • ‘uniform’ : uniform weights. All points in each neighborhood are weighted equally.
  • ‘distance’ : weight points by the inverse of their distance. in this case, closer neighbors of a query point will have a greater influence than neighbors which are further away.
  • [callable] : a user-defined function which accepts an array of distances, and returns an array of the same shape containing the weights.

Uniform weights are used by default.

algorithm : {‘auto’, ‘ball_tree’, ‘kd_tree’, ‘brute’}, optional

Algorithm used to compute the nearest neighbors:

  • ‘ball_tree’ will use BallTree
  • ‘kd_tree’ will use KDTree
  • ‘brute’ will use a brute-force search.
  • ‘auto’ will attempt to decide the most appropriate algorithm based on the values passed to fit() method.

Note: fitting on sparse input will override the setting of this parameter, using brute force.

leaf_size : int, optional (default = 30)
Leaf size passed to BallTree or KDTree. This can affect the speed of the construction and query, as well as the memory required to store the tree. The optimal value depends on the nature of the problem.
p : integer, optional (default = 2)
Power parameter for the Minkowski metric. When p = 1, this is equivalent to using manhattan_distance (l1), and euclidean_distance (l2) for p = 2. For arbitrary p, minkowski_distance (l_p) is used.
metric : string or callable, default ‘minkowski’
the distance metric to use for the tree. The default metric is minkowski, and with p=2 is equivalent to the standard Euclidean metric. See the documentation of the DistanceMetric class for a list of available metrics.
metric_params : dict, optional (default = None)
Additional keyword arguments for the metric function.
n_jobs : int or None, optional (default=None)
The number of parallel jobs to run for neighbors search. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details. Doesn’t affect fit() method.

Examples

>>> X = [[0], [1], [2], [3]]
>>> y = [0, 0, 1, 1]
>>> from sklearn.neighbors import KNeighborsRegressor
>>> neigh = KNeighborsRegressor(n_neighbors=2)
>>> neigh.fit(X, y) 
KNeighborsRegressor(...)
>>> print(neigh.predict([[1.5]]))
[0.5]

See also

NearestNeighbors RadiusNeighborsRegressor KNeighborsClassifier RadiusNeighborsClassifier

Notes

See Nearest Neighbors in the online documentation for a discussion of the choice of algorithm and leaf_size.

Warning

Regarding the Nearest Neighbors algorithms, if it is found that two neighbors, neighbor k+1 and k, have identical distances but different labels, the results will depend on the ordering of the training data.

https://en.wikipedia.org/wiki/K-nearest_neighbor_algorithm

Full API documentation: KNeighborsRegressorScikitsLearnNode

class mdp.nodes.LocalOutlierFactorScikitsLearnNode

Unsupervised Outlier Detection using Local Outlier Factor (LOF) This node has been automatically generated by wrapping the sklearn.neighbors.lof.LocalOutlierFactor class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. The anomaly score of each sample is called Local Outlier Factor. It measures the local deviation of density of a given sample with respect to its neighbors. It is local in that the anomaly score depends on how isolated the object is with respect to the surrounding neighborhood. More precisely, locality is given by k-nearest neighbors, whose distance is used to estimate the local density. By comparing the local density of a sample to the local densities of its neighbors, one can identify samples that have a substantially lower density than their neighbors. These are considered outliers.

Parameters

n_neighbors : int, optional (default=20)
Number of neighbors to use by default for kneighbors() queries. If n_neighbors is larger than the number of samples provided, all samples will be used.
algorithm : {‘auto’, ‘ball_tree’, ‘kd_tree’, ‘brute’}, optional

Algorithm used to compute the nearest neighbors:

  • ‘ball_tree’ will use BallTree
  • ‘kd_tree’ will use KDTree
  • ‘brute’ will use a brute-force search.
  • ‘auto’ will attempt to decide the most appropriate algorithm based on the values passed to fit() method.

Note: fitting on sparse input will override the setting of this parameter, using brute force.

leaf_size : int, optional (default=30)
Leaf size passed to BallTree or KDTree. This can affect the speed of the construction and query, as well as the memory required to store the tree. The optimal value depends on the nature of the problem.
metric : string or callable, default ‘minkowski’

metric used for the distance computation. Any metric from scikit-learn or scipy.spatial.distance can be used.

If ‘precomputed’, the training input X is expected to be a distance matrix.

If metric is a callable function, it is called on each pair of instances (rows) and the resulting value recorded. The callable should take two arrays as input and return one value indicating the distance between them. This works for Scipy’s metrics, but is less efficient than passing the metric name as a string.

Valid values for metric are:

  • from scikit-learn: [‘cityblock’, ‘cosine’, ‘euclidean’, ‘l1’, ‘l2’, ‘manhattan’]
  • from scipy.spatial.distance: [‘braycurtis’, ‘canberra’, ‘chebyshev’, ‘correlation’, ‘dice’, ‘hamming’, ‘jaccard’, ‘kulsinski’, ‘mahalanobis’, ‘minkowski’, ‘rogerstanimoto’, ‘russellrao’, ‘seuclidean’, ‘sokalmichener’, ‘sokalsneath’, ‘sqeuclidean’, ‘yule’]

See the documentation for scipy.spatial.distance for details on these metrics:

p : integer, optional (default=2)
Parameter for the Minkowski metric from sklearn.metrics.pairwise.pairwise_distances(). When p = 1, this is equivalent to using manhattan_distance (l1), and euclidean_distance (l2) for p = 2. For arbitrary p, minkowski_distance (l_p) is used.
metric_params : dict, optional (default=None)
Additional keyword arguments for the metric function.
contamination : float in (0., 0.5), optional (default=0.1)

The amount of contamination of the data set, i.e. the proportion of outliers in the data set. When fitting this is used to define the threshold on the decision function. If “auto”, the decision function threshold is determined as in the original paper.

Changed in version 0.20: The default value of contamination will change from 0.1 in 0.20 to 'auto' in 0.22.

novelty : boolean, default False
By default, LocalOutlierFactor is only meant to be used for outlier detection (novelty=False). Set novelty to True if you want to use LocalOutlierFactor for novelty detection. In this case be aware that that you should only use predict, decision_function and score_samples on new unseen data and not on the training set.
n_jobs : int or None, optional (default=None)
The number of parallel jobs to run for neighbors search. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details. Affects only kneighbors() and kneighbors_graph() methods.

Attributes

negative_outlier_factor_ : numpy array, shape (n_samples,)

The opposite LOF of the training samples. The higher, the more normal. Inliers tend to have a LOF score close to 1 (negative_outlier_factor_ close to -1), while outliers tend to have a larger LOF score.

The local outlier factor (LOF) of a sample captures its supposed ‘degree of abnormality’. It is the average of the ratio of the local reachability density of a sample and those of its k-nearest neighbors.

n_neighbors_ : integer
The actual number of neighbors used for kneighbors() queries.
offset_ : float
Offset used to obtain binary labels from the raw scores. Observations having a negative_outlier_factor smaller than offset_ are detected as abnormal. The offset is set to -1.5 (inliers score around -1), except when a contamination parameter different than “auto” is provided. In that case, the offset is defined in such a way we obtain the expected number of outliers in training.

References

[1]Breunig, M. M., Kriegel, H. P., Ng, R. T., & Sander, J. (2000, May). LOF: identifying density-based local outliers. In ACM sigmod record.

Full API documentation: LocalOutlierFactorScikitsLearnNode

class mdp.nodes.GaussianProcessRegressorScikitsLearnNode

Gaussian process regression (GPR). This node has been automatically generated by wrapping the sklearn.gaussian_process.gpr.GaussianProcessRegressor class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. The implementation is based on Algorithm 2.1 of Gaussian Processes for Machine Learning (GPML) by Rasmussen and Williams.

In addition to standard scikit-learn estimator API, GaussianProcessRegressor:

  • allows prediction without prior fitting (based on the GP prior)
  • provides an additional method sample_y(X), which evaluates samples drawn from the GPR (prior or posterior) at given inputs
  • exposes a method log_marginal_likelihood(theta), which can be used externally for other ways of selecting hyperparameters, e.g., via Markov chain Monte Carlo.

Read more in the User Guide.

New in version 0.18.

Parameters

kernel : kernel object
The kernel specifying the covariance function of the GP. If None is passed, the kernel “1.0 * RBF(1.0)” is used as default. Note that the kernel’s hyperparameters are optimized during fitting.
alpha : float or array-like, optional (default: 1e-10)
Value added to the diagonal of the kernel matrix during fitting. Larger values correspond to increased noise level in the observations. This can also prevent a potential numerical issue during fitting, by ensuring that the calculated values form a positive definite matrix. If an array is passed, it must have the same number of entries as the data used for fitting and is used as datapoint-dependent noise level. Note that this is equivalent to adding a WhiteKernel with c=alpha. Allowing to specify the noise level directly as a parameter is mainly for convenience and for consistency with Ridge.
optimizer : string or callable, optional (default: “fmin_l_bfgs_b”)

Can either be one of the internally supported optimizers for optimizing the kernel’s parameters, specified by a string, or an externally defined optimizer passed as a callable. If a callable is passed, it must have the signature:

def optimizer(obj_func, initial_theta, bounds):

    - # * 'obj_func' is the objective function to be minimized, which
    - #   takes the hyperparameters theta as parameter and an
    - #   optional flag eval_gradient, which determines if the
    - #   gradient is returned additionally to the function value
    - # * 'initial_theta': the initial value for theta, which can be
    - #   used by local optimizers
    - # * 'bounds': the bounds on the values of theta
    - ....
    - # Returned are the best found hyperparameters theta and
    - # the corresponding value of the target function.
    - return theta_opt, func_min

Per default, the ‘fmin_l_bfgs_b’ algorithm from scipy.optimize is used. If None is passed, the kernel’s parameters are kept fixed. Available internal optimizers are:

'fmin_l_bfgs_b'
n_restarts_optimizer : int, optional (default: 0)
The number of restarts of the optimizer for finding the kernel’s parameters which maximize the log-marginal likelihood. The first run of the optimizer is performed from the kernel’s initial parameters, the remaining ones (if any) from thetas sampled log-uniform randomly from the space of allowed theta-values. If greater than 0, all bounds must be finite. Note that n_restarts_optimizer == 0 implies that one run is performed.
normalize_y : boolean, optional (default: False)
Whether the target values y are normalized, i.e., the mean of the observed target values become zero. This parameter should be set to True if the target values’ mean is expected to differ considerable from zero. When enabled, the normalization effectively modifies the GP’s prior based on the data, which contradicts the likelihood principle; normalization is thus disabled per default.
copy_X_train : bool, optional (default: True)
If True, a persistent copy of the training data is stored in the object. Otherwise, just a reference to the training data is stored, which might cause predictions to change if the data is modified externally.
random_state : int, RandomState instance or None, optional (default: None)
The generator used to initialize the centers. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.

Attributes

X_train_ : array-like, shape = (n_samples, n_features)
Feature values in training data (also required for prediction)
y_train_ : array-like, shape = (n_samples, [n_output_dims])
Target values in training data (also required for prediction)
kernel_ : kernel object
The kernel used for prediction. The structure of the kernel is the same as the one passed as parameter but with optimized hyperparameters
L_ : array-like, shape = (n_samples, n_samples)
Lower-triangular Cholesky decomposition of the kernel in X_train_
alpha_ : array-like, shape = (n_samples,)
Dual coefficients of training data points in kernel space
log_marginal_likelihood_value_ : float
The log-marginal-likelihood of self.kernel_.theta

Examples

>>> from sklearn.datasets import make_friedman2
>>> from sklearn.gaussian_process import GaussianProcessRegressor
>>> from sklearn.gaussian_process.kernels import DotProduct, WhiteKernel
>>> X, y = make_friedman2(n_samples=500, noise=0, random_state=0)
>>> kernel = DotProduct() + WhiteKernel()
>>> gpr = GaussianProcessRegressor(kernel=kernel,
...         random_state=0).fit(X, y)
>>> gpr.score(X, y) 
0.3680...
>>> gpr.predict(X[:2,:], return_std=True) 
(array([653.0..., 592.1...]), array([316.6..., 316.6...]))

Full API documentation: GaussianProcessRegressorScikitsLearnNode

class mdp.nodes.KMeansScikitsLearnNode

K-Means clustering This node has been automatically generated by wrapping the sklearn.cluster.k_means_.KMeans class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Read more in the User Guide.

Parameters

n_clusters : int, optional, default: 8
The number of clusters to form as well as the number of centroids to generate.
init : {‘k-means++’, ‘random’ or an ndarray}

Method for initialization, defaults to ‘k-means++’:

‘k-means++’ : selects initial cluster centers for k-mean clustering in a smart way to speed up convergence. See section Notes in k_init for more details.

‘random’: choose k observations (rows) at random from data for the initial centroids.

If an ndarray is passed, it should be of shape (n_clusters, n_features) and gives the initial centers.

n_init : int, default: 10
Number of time the k-means algorithm will be run with different centroid seeds. The final results will be the best output of n_init consecutive runs in terms of inertia.
max_iter : int, default: 300
Maximum number of iterations of the k-means algorithm for a single run.
tol : float, default: 1e-4
Relative tolerance with regards to inertia to declare convergence
precompute_distances : {‘auto’, True, False}

Precompute distances (faster but takes more memory).

‘auto’ : do not precompute distances if n_samples * n_clusters > 12 million. This corresponds to about 100MB overhead per job using double precision.

True : always precompute distances

False : never precompute distances

verbose : int, default 0
Verbosity mode.
random_state : int, RandomState instance or None (default)
Determines random number generation for centroid initialization. Use an int to make the randomness deterministic. See Glossary.
copy_x : boolean, optional
When pre-computing distances it is more numerically accurate to center the data first. If copy_x is True (default), then the original data is not modified, ensuring X is C-contiguous. If False, the original data is modified, and put back before the function returns, but small numerical differences may be introduced by subtracting and then adding the data mean, in this case it will also not ensure that data is C-contiguous which may cause a significant slowdown.
n_jobs : int or None, optional (default=None)

The number of jobs to use for the computation. This works by computing each of the n_init runs in parallel.

None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.

algorithm : “auto”, “full” or “elkan”, default=”auto”
K-means algorithm to use. The classical EM-style algorithm is “full”. The “elkan” variation is more efficient by using the triangle inequality, but currently doesn’t support sparse data. “auto” chooses “elkan” for dense data and “full” for sparse data.

Attributes

cluster_centers_ : array, [n_clusters, n_features]
Coordinates of cluster centers. If the algorithm stops before fully converging (see tol and max_iter), these will not be consistent with labels_.

labels_ :

  • Labels of each point
inertia_ : float
Sum of squared distances of samples to their closest cluster center.
n_iter_ : int
Number of iterations run.

Examples

>>> from sklearn.cluster import KMeans
>>> import numpy as np
>>> X = np.array([[1, 2], [1, 4], [1, 0],
...               [10, 2], [10, 4], [10, 0]])
>>> kmeans = KMeans(n_clusters=2, random_state=0).fit(X)
>>> kmeans.labels_
array([1, 1, 1, 0, 0, 0], dtype=int32)
>>> kmeans.predict([[0, 0], [12, 3]])
array([1, 0], dtype=int32)
>>> kmeans.cluster_centers_
array([[10.,  2.],
       [ 1.,  2.]])

See also

MiniBatchKMeans
Alternative online implementation that does incremental updates of the centers positions using mini-batches. For large scale learning (say n_samples > 10k) MiniBatchKMeans is probably much faster than the default batch implementation.

Notes

The k-means problem is solved using either Lloyd’s or Elkan’s algorithm.

The average complexity is given by O(k n T), were n is the number of samples and T is the number of iteration.

The worst case complexity is given by O(n^(k+2/p)) with n = n_samples, p = n_features. (D. Arthur and S. Vassilvitskii, ‘How slow is the k-means method?’ SoCG2006)

In practice, the k-means algorithm is very fast (one of the fastest clustering algorithms available), but it falls in local minima. That’s why it can be useful to restart it several times.

If the algorithm stops before fully converging (because of tol or max_iter), labels_ and cluster_centers_ will not be consistent, i.e. the cluster_centers_ will not be the means of the points in each cluster. Also, the estimator will reassign labels_ after the last iteration to make labels_ consistent with predict on the training set.

Full API documentation: KMeansScikitsLearnNode

class mdp.nodes.OutputCodeClassifierScikitsLearnNode

(Error-Correcting) Output-Code multiclass strategy This node has been automatically generated by wrapping the sklearn.multiclass.OutputCodeClassifier class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Output-code based strategies consist in representing each class with a binary code (an array of 0s and 1s). At fitting time, one binary classifier per bit in the code book is fitted. At prediction time, the classifiers are used to project new points in the class space and the class closest to the points is chosen. The main advantage of these strategies is that the number of classifiers used can be controlled by the user, either for compressing the model (0 < code_size < 1) or for making the model more robust to errors (code_size > 1). See the documentation for more details.

Read more in the User Guide.

Parameters

estimator : estimator object
An estimator object implementing fit and one of decision_function or predict_proba.
code_size : float
Percentage of the number of classes to be used to create the code book. A number between 0 and 1 will require fewer classifiers than one-vs-the-rest. A number greater than 1 will require more classifiers than one-vs-the-rest.
random_state : int, RandomState instance or None, optional, default: None
The generator used to initialize the codebook. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.
n_jobs : int or None, optional (default=None)
The number of jobs to use for the computation. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.

Attributes

estimators_ : list of int(n_classes * code_size) estimators
Estimators used for predictions.
classes_ : numpy array of shape [n_classes]
Array containing labels.
code_book_ : numpy array of shape [n_classes, code_size]
Binary array containing the code of each class.

References

[1]“Solving multiclass learning problems via error-correcting output codes”, Dietterich T., Bakiri G., Journal of Artificial Intelligence Research 2, 1995.
[2]“The error coding method and PICTs”, James G., Hastie T., Journal of Computational and Graphical statistics 7, 1998.
[3]“The Elements of Statistical Learning”, Hastie T., Tibshirani R., Friedman J., page 606 (second-edition) 2008.

Full API documentation: OutputCodeClassifierScikitsLearnNode

class mdp.nodes.PassiveAggressiveRegressorScikitsLearnNode

Passive Aggressive Regressor This node has been automatically generated by wrapping the sklearn.linear_model.passive_aggressive.PassiveAggressiveRegressor class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Read more in the User Guide.

Parameters

C : float
Maximum step size (regularization). Defaults to 1.0.
fit_intercept : bool
Whether the intercept should be estimated or not. If False, the data is assumed to be already centered. Defaults to True.
max_iter : int, optional

The maximum number of passes over the training data (aka epochs). It only impacts the behavior in the fit method, and not the partial_fit. Defaults to 5. Defaults to 1000 from 0.21, or if tol is not None.

New in version 0.19.

tol : float or None, optional

The stopping criterion. If it is not None, the iterations will stop when (loss > previous_loss - tol). Defaults to None. Defaults to 1e-3 from 0.21.

New in version 0.19.

early_stopping : bool, default=False

Whether to use early stopping to terminate training when validation. score is not improving. If set to True, it will automatically set aside a fraction of training data as validation and terminate training when validation score is not improving by at least tol for n_iter_no_change consecutive epochs.

New in version 0.20.

validation_fraction : float, default=0.1

The proportion of training data to set aside as validation set for early stopping. Must be between 0 and 1. Only used if early_stopping is True.

New in version 0.20.

n_iter_no_change : int, default=5

Number of iterations with no improvement to wait before early stopping.

New in version 0.20.

shuffle : bool, default=True
Whether or not the training data should be shuffled after each epoch.
verbose : integer, optional
The verbosity level
loss : string, optional

The loss function to be used:

  • epsilon_insensitive: equivalent to PA-I in the reference paper.
  • squared_epsilon_insensitive: equivalent to PA-II in the reference
  • paper.
epsilon : float
If the difference between the current prediction and the correct label is below this threshold, the model is not updated.
random_state : int, RandomState instance or None, optional, default=None
The seed of the pseudo random number generator to use when shuffling the data. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.
warm_start : bool, optional

When set to True, reuse the solution of the previous call to fit as initialization, otherwise, just erase the previous solution. See the Glossary.

Repeatedly calling fit or partial_fit when warm_start is True can result in a different solution than when calling fit a single time because of the way the data is shuffled.

average : bool or int, optional

When set to True, computes the averaged SGD weights and stores the result in the coef_ attribute. If set to an int greater than 1, averaging will begin once the total number of samples seen reaches average. So average=10 will begin averaging after seeing 10 samples.

New in version 0.19: parameter average to use weights averaging in SGD

n_iter : int, optional

The number of passes over the training data (aka epochs). Defaults to None. Deprecated, will be removed in 0.21.

Changed in version 0.19: Deprecated

Attributes

coef_ : array, shape = [1, n_features] if n_classes == 2 else [n_classes, n_features]
Weights assigned to the features.
intercept_ : array, shape = [1] if n_classes == 2 else [n_classes]
Constants in decision function.
n_iter_ : int
The actual number of iterations to reach the stopping criterion.

Examples

>>> from sklearn.linear_model import PassiveAggressiveRegressor
>>> from sklearn.datasets import make_regression
>>> X, y = make_regression(n_features=4, random_state=0)
>>> regr = PassiveAggressiveRegressor(max_iter=100, random_state=0,
... tol=1e-3)
>>> regr.fit(X, y)
PassiveAggressiveRegressor(C=1.0, average=False, early_stopping=False,
              epsilon=0.1, fit_intercept=True, loss='epsilon_insensitive',
              max_iter=100, n_iter=None, n_iter_no_change=5,
              random_state=0, shuffle=True, tol=0.001,
              validation_fraction=0.1, verbose=0, warm_start=False)
>>> print(regr.coef_)
[20.48736655 34.18818427 67.59122734 87.94731329]
>>> print(regr.intercept_)
[-0.02306214]
>>> print(regr.predict([[0, 0, 0, 0]]))
[-0.02306214]

See also

SGDRegressor

References

Online Passive-Aggressive Algorithms <http://jmlr.csail.mit.edu/papers/volume7/crammer06a/crammer06a.pdf> K. Crammer, O. Dekel, J. Keshat, S. Shalev-Shwartz, Y. Singer - JMLR (2006)

Full API documentation: PassiveAggressiveRegressorScikitsLearnNode

class mdp.nodes.RandomForestClassifierScikitsLearnNode

A random forest classifier. This node has been automatically generated by wrapping the sklearn.ensemble.forest.RandomForestClassifier class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. A random forest is a meta estimator that fits a number of decision tree classifiers on various sub-samples of the dataset and uses averaging to improve the predictive accuracy and control over-fitting. The sub-sample size is always the same as the original input sample size but the samples are drawn with replacement if bootstrap=True (default).

Read more in the User Guide.

Parameters

n_estimators : integer, optional (default=10)

The number of trees in the forest.

Changed in version 0.20: The default value of n_estimators will change from 10 in version 0.20 to 100 in version 0.22.

criterion : string, optional (default=”gini”)
The function to measure the quality of a split. Supported criteria are “gini” for the Gini impurity and “entropy” for the information gain. Note: this parameter is tree-specific.
max_depth : integer or None, optional (default=None)
The maximum depth of the tree. If None, then nodes are expanded until all leaves are pure or until all leaves contain less than min_samples_split samples.
min_samples_split : int, float, optional (default=2)

The minimum number of samples required to split an internal node:

  • If int, then consider min_samples_split as the minimum number.
  • If float, then min_samples_split is a fraction and ceil(min_samples_split * n_samples) are the minimum number of samples for each split.

Changed in version 0.18: Added float values for fractions.

min_samples_leaf : int, float, optional (default=1)

The minimum number of samples required to be at a leaf node. A split point at any depth will only be considered if it leaves at least min_samples_leaf training samples in each of the left and right branches. This may have the effect of smoothing the model, especially in regression.

  • If int, then consider min_samples_leaf as the minimum number.
  • If float, then min_samples_leaf is a fraction and ceil(min_samples_leaf * n_samples) are the minimum number of samples for each node.

Changed in version 0.18: Added float values for fractions.

min_weight_fraction_leaf : float, optional (default=0.)
The minimum weighted fraction of the sum total of weights (of all the input samples) required to be at a leaf node. Samples have equal weight when sample_weight is not provided.
max_features : int, float, string or None, optional (default=”auto”)

The number of features to consider when looking for the best split:

  • If int, then consider max_features features at each split.
  • If float, then max_features is a fraction and int(max_features * n_features) features are considered at each split.
  • If “auto”, then max_features=sqrt(n_features).
  • If “sqrt”, then max_features=sqrt(n_features) (same as “auto”).
  • If “log2”, then max_features=log2(n_features).
  • If None, then max_features=n_features.

Note: the search for a split does not stop until at least one valid partition of the node samples is found, even if it requires to effectively inspect more than max_features features.

max_leaf_nodes : int or None, optional (default=None)
Grow trees with max_leaf_nodes in best-first fashion. Best nodes are defined as relative reduction in impurity. If None then unlimited number of leaf nodes.
min_impurity_decrease : float, optional (default=0.)

A node will be split if this split induces a decrease of the impurity greater than or equal to this value.

The weighted impurity decrease equation is the following:

N_t / N * (impurity - N_t_R / N_t * right_impurity
                    - N_t_L / N_t * left_impurity)

where N is the total number of samples, N_t is the number of samples at the current node, N_t_L is the number of samples in the left child, and N_t_R is the number of samples in the right child.

N, N_t, N_t_R and N_t_L all refer to the weighted sum, if sample_weight is passed.

New in version 0.19.

min_impurity_split : float, (default=1e-7)

Threshold for early stopping in tree growth. A node will split if its impurity is above the threshold, otherwise it is a leaf.

Deprecated since version 0.19: min_impurity_split has been deprecated in favor of min_impurity_decrease in 0.19. The default value of min_impurity_split will change from 1e-7 to 0 in 0.23 and it will be removed in 0.25. Use min_impurity_decrease instead.

bootstrap : boolean, optional (default=True)
Whether bootstrap samples are used when building trees. If False, the whole datset is used to build each tree.
oob_score : bool (default=False)
Whether to use out-of-bag samples to estimate the generalization accuracy.
n_jobs : int or None, optional (default=None)
The number of jobs to run in parallel for both fit and predict. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
random_state : int, RandomState instance or None, optional (default=None)
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.
verbose : int, optional (default=0)
Controls the verbosity when fitting and predicting.
warm_start : bool, optional (default=False)
When set to True, reuse the solution of the previous call to fit and add more estimators to the ensemble, otherwise, just fit a whole new forest. See the Glossary.
class_weight : dict, list of dicts, “balanced”, “balanced_subsample” or None, optional (default=None)

Weights associated with classes in the form {class_label: weight}. If not given, all classes are supposed to have weight one. For multi-output problems, a list of dicts can be provided in the same order as the columns of y.

Note that for multioutput (including multilabel) weights should be defined for each class of every column in its own dict. For example, for four-class multilabel classification weights should be [{0: 1, 1: 1}, {0: 1, 1: 5}, {0: 1, 1: 1}, {0: 1, 1: 1}] instead of [{1:1}, {2:5}, {3:1}, {4:1}].

The “balanced” mode uses the values of y to automatically adjust weights inversely proportional to class frequencies in the input data as n_samples / (n_classes * np.bincount(y))

The “balanced_subsample” mode is the same as “balanced” except that weights are computed based on the bootstrap sample for every tree grown.

For multi-output, the weights of each column of y will be multiplied.

Note that these weights will be multiplied with sample_weight (passed through the fit method) if sample_weight is specified.

Attributes

estimators_ : list of DecisionTreeClassifier
The collection of fitted sub-estimators.
classes_ : array of shape = [n_classes] or a list of such arrays
The classes labels (single output problem), or a list of arrays of class labels (multi-output problem).
n_classes_ : int or list
The number of classes (single output problem), or a list containing the number of classes for each output (multi-output problem).
n_features_ : int
The number of features when fit is performed.
n_outputs_ : int
The number of outputs when fit is performed.
feature_importances_ : array of shape = [n_features]
The feature importances (the higher, the more important the feature).
oob_score_ : float
Score of the training dataset obtained using an out-of-bag estimate.
oob_decision_function_ : array of shape = [n_samples, n_classes]
Decision function computed with out-of-bag estimate on the training set. If n_estimators is small it might be possible that a data point was never left out during the bootstrap. In this case, oob_decision_function_ might contain NaN.

Examples

>>> from sklearn.ensemble import RandomForestClassifier
>>> from sklearn.datasets import make_classification
>>> X, y = make_classification(n_samples=1000, n_features=4,
...                            n_informative=2, n_redundant=0,
...                            random_state=0, shuffle=False)
>>> clf = RandomForestClassifier(n_estimators=100, max_depth=2,
...                              random_state=0)
>>> clf.fit(X, y)
RandomForestClassifier(bootstrap=True, class_weight=None, criterion='gini',
            max_depth=2, max_features='auto', max_leaf_nodes=None,
            min_impurity_decrease=0.0, min_impurity_split=None,
            min_samples_leaf=1, min_samples_split=2,
            min_weight_fraction_leaf=0.0, n_estimators=100, n_jobs=None,
            oob_score=False, random_state=0, verbose=0, warm_start=False)
>>> print(clf.feature_importances_)
[0.14205973 0.76664038 0.0282433  0.06305659]
>>> print(clf.predict([[0, 0, 0, 0]]))
[1]

Notes

The default values for the parameters controlling the size of the trees (e.g. max_depth, min_samples_leaf, etc.) lead to fully grown and unpruned trees which can potentially be very large on some data sets. To reduce memory consumption, the complexity and size of the trees should be controlled by setting those parameter values.

The features are always randomly permuted at each split. Therefore, the best found split may vary, even with the same training data, max_features=n_features and bootstrap=False, if the improvement of the criterion is identical for several splits enumerated during the search of the best split. To obtain a deterministic behaviour during fitting, random_state has to be fixed.

References

[1]
  1. Breiman, “Random Forests”, Machine Learning, 45(1), 5-32, 2001.

See also

DecisionTreeClassifier, ExtraTreesClassifier

Full API documentation: RandomForestClassifierScikitsLearnNode

class mdp.nodes.ForestRegressorScikitsLearnNode

Base class for forest of trees-based regressors. This node has been automatically generated by wrapping the sklearn.ensemble.forest.ForestRegressor class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Warning: This class should not be used directly. Use derived classes instead.

Full API documentation: ForestRegressorScikitsLearnNode

class mdp.nodes.RidgeScikitsLearnNode

Linear least squares with l2 regularization. This node has been automatically generated by wrapping the sklearn.linear_model.ridge.Ridge class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Minimizes the objective function:

||y - Xw||^2_2 + alpha * ||w||^2_2

This model solves a regression model where the loss function is the linear least squares function and regularization is given by the l2-norm. Also known as Ridge Regression or Tikhonov regularization. This estimator has built-in support for multi-variate regression (i.e., when y is a 2d-array of shape [n_samples, n_targets]).

Read more in the User Guide.

Parameters

alpha : {float, array-like}, shape (n_targets)
Regularization strength; must be a positive float. Regularization improves the conditioning of the problem and reduces the variance of the estimates. Larger values specify stronger regularization. Alpha corresponds to C^-1 in other linear models such as LogisticRegression or LinearSVC. If an array is passed, penalties are assumed to be specific to the targets. Hence they must correspond in number.
fit_intercept : boolean
Whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (e.g. data is expected to be already centered).
normalize : boolean, optional, default False
This parameter is ignored when fit_intercept is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use sklearn.preprocessing.StandardScaler before calling fit on an estimator with normalize=False.
copy_X : boolean, optional, default True
If True, X will be copied; else, it may be overwritten.
max_iter : int, optional
Maximum number of iterations for conjugate gradient solver. For ‘sparse_cg’ and ‘lsqr’ solvers, the default value is determined by scipy.sparse.linalg. For ‘sag’ solver, the default value is 1000.
tol : float
Precision of the solution.
solver : {‘auto’, ‘svd’, ‘cholesky’, ‘lsqr’, ‘sparse_cg’, ‘sag’, ‘saga’}

Solver to use in the computational routines:

  • ‘auto’ chooses the solver automatically based on the type of data.
  • ‘svd’ uses a Singular Value Decomposition of X to compute the Ridge coefficients. More stable for singular matrices than ‘cholesky’.
  • ‘cholesky’ uses the standard scipy.linalg.solve function to obtain a closed-form solution.
  • ‘sparse_cg’ uses the conjugate gradient solver as found in scipy.sparse.linalg.cg. As an iterative algorithm, this solver is more appropriate than ‘cholesky’ for large-scale data (possibility to set tol and max_iter).
  • ‘lsqr’ uses the dedicated regularized least-squares routine scipy.sparse.linalg.lsqr. It is the fastest and uses an iterative procedure.
  • ‘sag’ uses a Stochastic Average Gradient descent, and ‘saga’ uses its improved, unbiased version named SAGA. Both methods also use an iterative procedure, and are often faster than other solvers when both n_samples and n_features are large. Note that ‘sag’ and ‘saga’ fast convergence is only guaranteed on features with approximately the same scale. You can preprocess the data with a scaler from sklearn.preprocessing.

All last five solvers support both dense and sparse data. However, only ‘sag’ and ‘saga’ supports sparse input when fit_intercept is True.

New in version 0.17: Stochastic Average Gradient descent solver.

New in version 0.19: SAGA solver.

random_state : int, RandomState instance or None, optional, default None

The seed of the pseudo random number generator to use when shuffling the data. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random. Used when solver == ‘sag’.

New in version 0.17: random_state to support Stochastic Average Gradient.

Attributes

coef_ : array, shape (n_features,) or (n_targets, n_features)
Weight vector(s).
intercept_ : float | array, shape = (n_targets,)
Independent term in decision function. Set to 0.0 if fit_intercept = False.
n_iter_ : array or None, shape (n_targets,)

Actual number of iterations for each target. Available only for sag and lsqr solvers. Other solvers will return None.

New in version 0.17.

See also

RidgeClassifier : Ridge classifier RidgeCV : Ridge regression with built-in cross validation sklearn.kernel_ridge.KernelRidge : Kernel ridge regression

combines ridge regression with the kernel trick

Examples

>>> from sklearn.linear_model import Ridge
>>> import numpy as np
>>> n_samples, n_features = 10, 5
>>> np.random.seed(0)
>>> y = np.random.randn(n_samples)
>>> X = np.random.randn(n_samples, n_features)
>>> clf = Ridge(alpha=1.0)
>>> clf.fit(X, y) 
Ridge(alpha=1.0, copy_X=True, fit_intercept=True, max_iter=None,
      normalize=False, random_state=None, solver='auto', tol=0.001)

Full API documentation: RidgeScikitsLearnNode

class mdp.nodes.ElasticNetScikitsLearnNode

Linear regression with combined L1 and L2 priors as regularizer. This node has been automatically generated by wrapping the sklearn.linear_model.coordinate_descent.ElasticNet class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Minimizes the objective function:

1 / (2 * n_samples) * ||y - Xw||^2_2
+ alpha * l1_ratio * ||w||_1
+ 0.5 * alpha * (1 - l1_ratio) * ||w||^2_2

If you are interested in controlling the L1 and L2 penalty separately, keep in mind that this is equivalent to:

a * L1 + b * L2

where:

alpha = a + b and l1_ratio = a / (a + b)

The parameter l1_ratio corresponds to alpha in the glmnet R package while alpha corresponds to the lambda parameter in glmnet. Specifically, l1_ratio = 1 is the lasso penalty. Currently, l1_ratio <= 0.01 is not reliable, unless you supply your own sequence of alpha.

Read more in the User Guide.

Parameters

alpha : float, optional
Constant that multiplies the penalty terms. Defaults to 1.0. See the notes for the exact mathematical meaning of this parameter.``alpha = 0`` is equivalent to an ordinary least square, solved by the LinearRegression object. For numerical reasons, using alpha = 0 with the Lasso object is not advised. Given this, you should use the LinearRegression object.
l1_ratio : float
The ElasticNet mixing parameter, with 0 <= l1_ratio <= 1. For l1_ratio = 0 the penalty is an L2 penalty. For l1_ratio = 1 it is an L1 penalty. For 0 < l1_ratio < 1, the penalty is a combination of L1 and L2.
fit_intercept : bool
Whether the intercept should be estimated or not. If False, the data is assumed to be already centered.
normalize : boolean, optional, default False
This parameter is ignored when fit_intercept is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use sklearn.preprocessing.StandardScaler before calling fit on an estimator with normalize=False.
precompute : True | False | array-like
Whether to use a precomputed Gram matrix to speed up calculations. The Gram matrix can also be passed as argument. For sparse input this option is always True to preserve sparsity.
max_iter : int, optional
The maximum number of iterations
copy_X : boolean, optional, default True
If True, X will be copied; else, it may be overwritten.
tol : float, optional
The tolerance for the optimization: if the updates are smaller than tol, the optimization code checks the dual gap for optimality and continues until it is smaller than tol.
warm_start : bool, optional
When set to True, reuse the solution of the previous call to fit as initialization, otherwise, just erase the previous solution. See the Glossary.
positive : bool, optional
When set to True, forces the coefficients to be positive.
random_state : int, RandomState instance or None, optional, default None
The seed of the pseudo random number generator that selects a random feature to update. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random. Used when selection == ‘random’.
selection : str, default ‘cyclic’
If set to ‘random’, a random coefficient is updated every iteration rather than looping over features sequentially by default. This (setting to ‘random’) often leads to significantly faster convergence especially when tol is higher than 1e-4.

Attributes

coef_ : array, shape (n_features,) | (n_targets, n_features)
parameter vector (w in the cost function formula)
sparse_coef_ : scipy.sparse matrix, shape (n_features, 1) | (n_targets, n_features)
sparse_coef_ is a readonly property derived from coef_
intercept_ : float | array, shape (n_targets,)
independent term in decision function.
n_iter_ : array-like, shape (n_targets,)
number of iterations run by the coordinate descent solver to reach the specified tolerance.

Examples

>>> from sklearn.linear_model import ElasticNet
>>> from sklearn.datasets import make_regression
>>> X, y = make_regression(n_features=2, random_state=0)
>>> regr = ElasticNet(random_state=0)
>>> regr.fit(X, y)
ElasticNet(alpha=1.0, copy_X=True, fit_intercept=True, l1_ratio=0.5,
      max_iter=1000, normalize=False, positive=False, precompute=False,
      random_state=0, selection='cyclic', tol=0.0001, warm_start=False)
>>> print(regr.coef_) 
[18.83816048 64.55968825]
>>> print(regr.intercept_) 
1.451...
>>> print(regr.predict([[0, 0]])) 
[1.451...]

Notes

To avoid unnecessary memory duplication the X argument of the fit method should be directly passed as a Fortran-contiguous numpy array.

See also

ElasticNetCV : Elastic net model with best model selection by
cross-validation.

SGDRegressor: implements elastic net regression with incremental training. SGDClassifier: implements logistic regression with elastic net penalty

(SGDClassifier(loss="log", penalty="elasticnet")).

Full API documentation: ElasticNetScikitsLearnNode

class mdp.nodes.IsomapScikitsLearnNode

Isomap Embedding This node has been automatically generated by wrapping the sklearn.manifold.isomap.Isomap class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Non-linear dimensionality reduction through Isometric Mapping

Read more in the User Guide.

Parameters

n_neighbors : integer
number of neighbors to consider for each point.
n_components : integer
number of coordinates for the manifold
eigen_solver : [‘auto’|’arpack’|’dense’]

‘auto’ : Attempt to choose the most efficient solver for the given problem.

‘arpack’ : Use Arnoldi decomposition to find the eigenvalues and eigenvectors.

‘dense’ : Use a direct solver (i.e. LAPACK) for the eigenvalue decomposition.

tol : float
Convergence tolerance passed to arpack or lobpcg. not used if eigen_solver == ‘dense’.
max_iter : integer
Maximum number of iterations for the arpack solver. not used if eigen_solver == ‘dense’.
path_method : string [‘auto’|’FW’|’D’]

Method to use in finding shortest path.

‘auto’ : attempt to choose the best algorithm automatically.

‘FW’ : Floyd-Warshall algorithm.

‘D’ : Dijkstra’s algorithm.

neighbors_algorithm : string [‘auto’|’brute’|’kd_tree’|’ball_tree’]
Algorithm to use for nearest neighbors search, passed to neighbors.NearestNeighbors instance.
n_jobs : int or None, optional (default=None)
The number of parallel jobs to run. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.

Attributes

embedding_ : array-like, shape (n_samples, n_components)
Stores the embedding vectors.
kernel_pca_ : object
KernelPCA object used to implement the embedding.
training_data_ : array-like, shape (n_samples, n_features)
Stores the training data.
nbrs_ : sklearn.neighbors.NearestNeighbors instance
Stores nearest neighbors instance, including BallTree or KDtree if applicable.
dist_matrix_ : array-like, shape (n_samples, n_samples)
Stores the geodesic distance matrix of training data.

Examples

>>> from sklearn.datasets import load_digits
>>> from sklearn.manifold import Isomap
>>> X, _ = load_digits(return_X_y=True)
>>> X.shape
(1797, 64)
>>> embedding = Isomap(n_components=2)
>>> X_transformed = embedding.fit_transform(X[:100])
>>> X_transformed.shape
(100, 2)

References

[1]Tenenbaum, J.B.; De Silva, V.; & Langford, J.C. A global geometric framework for nonlinear dimensionality reduction. Science 290 (5500)

Full API documentation: IsomapScikitsLearnNode

class mdp.nodes.BinarizerScikitsLearnNode

Binarize data (set feature values to 0 or 1) according to a threshold This node has been automatically generated by wrapping the sklearn.preprocessing.data.Binarizer class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Values greater than the threshold map to 1, while values less than or equal to the threshold map to 0. With the default threshold of 0, only positive values map to 1.

Binarization is a common operation on text count data where the analyst can decide to only consider the presence or absence of a feature rather than a quantified number of occurrences for instance.

It can also be used as a pre-processing step for estimators that consider boolean random variables (e.g. modelled using the Bernoulli distribution in a Bayesian setting).

Read more in the User Guide.

Parameters

threshold : float, optional (0.0 by default)
Feature values below or equal to this are replaced by 0, above it by 1. Threshold may not be less than 0 for operations on sparse matrices.
copy : boolean, optional, default True
set to False to perform inplace binarization and avoid a copy (if the input is already a numpy array or a scipy.sparse CSR matrix).

Examples

>>> from sklearn.preprocessing import Binarizer
>>> X = [[ 1., -1.,  2.],
...      [ 2.,  0.,  0.],
...      [ 0.,  1., -1.]]
>>> transformer = Binarizer().fit(X) # fit does nothing.
>>> transformer
Binarizer(copy=True, threshold=0.0)
>>> transformer.transform(X)
array([[1., 0., 1.],
       [1., 0., 0.],
       [0., 1., 0.]])

Notes

If the input is a sparse matrix, only the non-zero values are subject to update by the Binarizer class.

This estimator is stateless (besides constructor parameters), the fit method does nothing but is useful when used in a pipeline.

See also

binarize: Equivalent function without the estimator API.

Full API documentation: BinarizerScikitsLearnNode

class mdp.nodes.MiniBatchDictionaryLearningScikitsLearnNode

Mini-batch dictionary learning This node has been automatically generated by wrapping the sklearn.decomposition.dict_learning.MiniBatchDictionaryLearning class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Finds a dictionary (a set of atoms) that can best be used to represent data using a sparse code.

Solves the optimization problem:

(U^*,V^*) = argmin 0.5 || Y - U V ||_2^2 + alpha * || U ||_1
             (U,V)
             with || V_k ||_2 = 1 for all  0 <= k < n_components

Read more in the User Guide.

Parameters

n_components : int,
number of dictionary elements to extract
alpha : float,
sparsity controlling parameter
n_iter : int,
total number of iterations to perform
fit_algorithm : {‘lars’, ‘cd’}
lars: uses the least angle regression method to solve the lasso problem (linear_model.lars_path) cd: uses the coordinate descent method to compute the Lasso solution (linear_model.Lasso). Lars will be faster if the estimated components are sparse.
n_jobs : int or None, optional (default=None)
Number of parallel jobs to run. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
batch_size : int,
number of samples in each mini-batch
shuffle : bool,
whether to shuffle the samples before forming batches
dict_init : array of shape (n_components, n_features),
initial value of the dictionary for warm restart scenarios
transform_algorithm : {‘lasso_lars’, ‘lasso_cd’, ‘lars’, ‘omp’, ‘threshold’}
Algorithm used to transform the data. lars: uses the least angle regression method (linear_model.lars_path) lasso_lars: uses Lars to compute the Lasso solution lasso_cd: uses the coordinate descent method to compute the Lasso solution (linear_model.Lasso). lasso_lars will be faster if the estimated components are sparse. omp: uses orthogonal matching pursuit to estimate the sparse solution threshold: squashes to zero all coefficients less than alpha from the projection dictionary * X’
transform_n_nonzero_coefs : int, 0.1 * n_features by default
Number of nonzero coefficients to target in each column of the solution. This is only used by algorithm=’lars’ and algorithm=’omp’ and is overridden by alpha in the omp case.
transform_alpha : float, 1. by default
If algorithm=’lasso_lars’ or algorithm=’lasso_cd’, alpha is the penalty applied to the L1 norm. If algorithm=’threshold’, alpha is the absolute value of the threshold below which coefficients will be squashed to zero. If algorithm=’omp’, alpha is the tolerance parameter: the value of the reconstruction error targeted. In this case, it overrides n_nonzero_coefs.
verbose : bool, optional (default: False)
To control the verbosity of the procedure.
split_sign : bool, False by default
Whether to split the sparse feature vector into the concatenation of its negative part and its positive part. This can improve the performance of downstream classifiers.
random_state : int, RandomState instance or None, optional (default=None)
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.
positive_code : bool

Whether to enforce positivity when finding the code.

New in version 0.20.

positive_dict : bool

Whether to enforce positivity when finding the dictionary.

New in version 0.20.

Attributes

components_ : array, [n_components, n_features]
components extracted from the data
inner_stats_ : tuple of (A, B) ndarrays
Internal sufficient statistics that are kept by the algorithm. Keeping them is useful in online settings, to avoid loosing the history of the evolution, but they shouldn’t have any use for the end user. A (n_components, n_components) is the dictionary covariance matrix. B (n_features, n_components) is the data approximation matrix
n_iter_ : int
Number of iterations run.

Notes

References:

J. Mairal, F. Bach, J. Ponce, G. Sapiro, 2009: Online dictionary learning for sparse coding (http://www.di.ens.fr/sierra/pdfs/icml09.pdf)

See also

SparseCoder DictionaryLearning SparsePCA MiniBatchSparsePCA

Full API documentation: MiniBatchDictionaryLearningScikitsLearnNode

class mdp.nodes.TfidfVectorizerScikitsLearnNode

Convert a collection of raw documents to a matrix of TF-IDF features. This node has been automatically generated by wrapping the sklearn.feature_extraction.text.TfidfVectorizer class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Equivalent to CountVectorizer followed by TfidfTransformer.

Read more in the User Guide.

Parameters

input : string {‘filename’, ‘file’, ‘content’}

If ‘filename’, the sequence passed as an argument to fit is expected to be a list of filenames that need reading to fetch the raw content to analyze.

If ‘file’, the sequence items must have a ‘read’ method (file-like object) that is called to fetch the bytes in memory.

Otherwise the input is expected to be the sequence strings or bytes items are expected to be analyzed directly.

encoding : string, ‘utf-8’ by default.
If bytes or files are given to analyze, this encoding is used to decode.
decode_error : {‘strict’, ‘ignore’, ‘replace’} (default=’strict’)
Instruction on what to do if a byte sequence is given to analyze that contains characters not of the given encoding. By default, it is ‘strict’, meaning that a UnicodeDecodeError will be raised. Other values are ‘ignore’ and ‘replace’.
strip_accents : {‘ascii’, ‘unicode’, None} (default=None)

Remove accents and perform other character normalization during the preprocessing step. ‘ascii’ is a fast method that only works on characters that have an direct ASCII mapping. ‘unicode’ is a slightly slower method that works on any characters. None (default) does nothing.

Both ‘ascii’ and ‘unicode’ use NFKD normalization from unicodedata.normalize().

lowercase : boolean (default=True)
Convert all characters to lowercase before tokenizing.
preprocessor : callable or None (default=None)
Override the preprocessing (string transformation) stage while preserving the tokenizing and n-grams generation steps.
tokenizer : callable or None (default=None)
Override the string tokenization step while preserving the preprocessing and n-grams generation steps. Only applies if analyzer == 'word'.
analyzer : string, {‘word’, ‘char’, ‘char_wb’} or callable

Whether the feature should be made of word or character n-grams. Option ‘char_wb’ creates character n-grams only from text inside word boundaries; n-grams at the edges of words are padded with space.

If a callable is passed it is used to extract the sequence of features out of the raw, unprocessed input.

stop_words : string {‘english’}, list, or None (default=None)

If a string, it is passed to _check_stop_list and the appropriate stop list is returned. ‘english’ is currently the only supported string value. There are several known issues with ‘english’ and you should consider an alternative (see stop_words).

If a list, that list is assumed to contain stop words, all of which will be removed from the resulting tokens. Only applies if analyzer == 'word'.

If None, no stop words will be used. max_df can be set to a value in the range [0.7, 1.0) to automatically detect and filter stop words based on intra corpus document frequency of terms.

token_pattern : string
Regular expression denoting what constitutes a “token”, only used if analyzer == 'word'. The default regexp selects tokens of 2 or more alphanumeric characters (punctuation is completely ignored and always treated as a token separator).
ngram_range : tuple (min_n, max_n) (default=(1, 1))
The lower and upper boundary of the range of n-values for different n-grams to be extracted. All values of n such that min_n <= n <= max_n will be used.
max_df : float in range [0.0, 1.0] or int (default=1.0)
When building the vocabulary ignore terms that have a document frequency strictly higher than the given threshold (corpus-specific stop words). If float, the parameter represents a proportion of documents, integer absolute counts. This parameter is ignored if vocabulary is not None.
min_df : float in range [0.0, 1.0] or int (default=1)
When building the vocabulary ignore terms that have a document frequency strictly lower than the given threshold. This value is also called cut-off in the literature. If float, the parameter represents a proportion of documents, integer absolute counts. This parameter is ignored if vocabulary is not None.
max_features : int or None (default=None)

If not None, build a vocabulary that only consider the top max_features ordered by term frequency across the corpus.

This parameter is ignored if vocabulary is not None.

vocabulary : Mapping or iterable, optional (default=None)
Either a Mapping (e.g., a dict) where keys are terms and values are indices in the feature matrix, or an iterable over terms. If not given, a vocabulary is determined from the input documents.
binary : boolean (default=False)
If True, all non-zero term counts are set to 1. This does not mean outputs will have only 0/1 values, only that the tf term in tf-idf is binary. (Set idf and normalization to False to get 0/1 outputs.)
dtype : type, optional (default=float64)
Type of the matrix returned by fit_transform() or transform().
norm : ‘l1’, ‘l2’ or None, optional (default=’l2’)

Each output row will have unit norm, either:

    • ‘l2’: Sum of squares of vector elements is 1. The cosine
  • similarity between two vectors is their dot product when l2 norm has
  • been applied.
    • ‘l1’: Sum of absolute values of vector elements is 1.
  • See preprocessing.normalize()
use_idf : boolean (default=True)
Enable inverse-document-frequency reweighting.
smooth_idf : boolean (default=True)
Smooth idf weights by adding one to document frequencies, as if an extra document was seen containing every term in the collection exactly once. Prevents zero divisions.
sublinear_tf : boolean (default=False)
Apply sublinear tf scaling, i.e. replace tf with 1 + log(tf).

Attributes

vocabulary_ : dict
A mapping of terms to feature indices.
idf_ : array, shape (n_features)
The inverse document frequency (IDF) vector; only defined if use_idf is True.
stop_words_ : set

Terms that were ignored because they either:

  • occurred in too many documents (max_df)
  • occurred in too few documents (min_df)
  • were cut off by feature selection (max_features).

This is only available if no vocabulary was given.

Examples

>>> from sklearn.feature_extraction.text import TfidfVectorizer
>>> corpus = [
...     'This is the first document.',
...     'This document is the second document.',
...     'And this is the third one.',
...     'Is this the first document?',
... ]
>>> vectorizer = TfidfVectorizer()
>>> X = vectorizer.fit_transform(corpus)
>>> print(vectorizer.get_feature_names())
['and', 'document', 'first', 'is', 'one', 'second', 'the', 'third', 'this']
>>> print(X.shape)
(4, 9)

See also

CountVectorizer : Transforms text into a sparse matrix of n-gram counts.

TfidfTransformer : Performs the TF-IDF transformation from a provided
matrix of counts.

Notes

The stop_words_ attribute can get large and increase the model size when pickling. This attribute is provided only for introspection and can be safely removed using delattr or set to None before pickling.

Full API documentation: TfidfVectorizerScikitsLearnNode

class mdp.nodes.KBinsDiscretizerScikitsLearnNode

Bin continuous data into intervals. This node has been automatically generated by wrapping the sklearn.preprocessing._discretization.KBinsDiscretizer class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Read more in the User Guide.

Parameters

n_bins : int or array-like, shape (n_features,) (default=5)
The number of bins to produce. Raises ValueError if n_bins < 2.
encode : {‘onehot’, ‘onehot-dense’, ‘ordinal’}, (default=’onehot’)

Method used to encode the transformed result.

onehot
Encode the transformed result with one-hot encoding and return a sparse matrix. Ignored features are always stacked to the right.
onehot-dense
Encode the transformed result with one-hot encoding and return a dense array. Ignored features are always stacked to the right.
ordinal
Return the bin identifier encoded as an integer value.
strategy : {‘uniform’, ‘quantile’, ‘kmeans’}, (default=’quantile’)

Strategy used to define the widths of the bins.

uniform
All bins in each feature have identical widths.
quantile
All bins in each feature have the same number of points.
kmeans
Values in each bin have the same nearest center of a 1D k-means cluster.

Attributes

n_bins_ : int array, shape (n_features,)
Number of bins per feature. Bins whose width are too small (i.e., <= 1e-8) are removed with a warning.
bin_edges_ : array of arrays, shape (n_features, )
The edges of each bin. Contain arrays of varying shapes (n_bins_, ) Ignored features will have empty arrays.

Examples

>>> X = [[-2, 1, -4,   -1],
...      [-1, 2, -3, -0.5],
...      [ 0, 3, -2,  0.5],
...      [ 1, 4, -1,    2]]
>>> est = KBinsDiscretizer(n_bins=3, encode='ordinal', strategy='uniform')
>>> est.fit(X)  
KBinsDiscretizer(...)
>>> Xt = est.transform(X)
>>> Xt  
array([[ 0., 0., 0., 0.],
       [ 1., 1., 1., 0.],
       [ 2., 2., 2., 1.],
       [ 2., 2., 2., 2.]])

Sometimes it may be useful to convert the data back into the original feature space. The inverse_transform function converts the binned data into the original feature space. Each value will be equal to the mean of the two bin edges.

>>> est.bin_edges_[0]
array([-2., -1.,  0.,  1.])
>>> est.inverse_transform(Xt)
array([[-1.5,  1.5, -3.5, -0.5],
       [-0.5,  2.5, -2.5, -0.5],
       [ 0.5,  3.5, -1.5,  0.5],
       [ 0.5,  3.5, -1.5,  1.5]])

Notes

In bin edges for feature i, the first and last values are used only for inverse_transform. During transform, bin edges are extended to:

np.concatenate([-np.inf, bin_edges_[i][1:-1], np.inf])

You can combine KBinsDiscretizer with sklearn.compose.ColumnTransformer if you only want to preprocess part of the features.

KBinsDiscretizer might produce constant features (e.g., when encode = 'onehot' and certain bins do not contain any data). These features can be removed with feature selection algorithms (e.g., sklearn.feature_selection.VarianceThreshold).

See also

sklearn.preprocessing.Binarizer : class used to bin values as 0 or
1 based on a parameter threshold.

Full API documentation: KBinsDiscretizerScikitsLearnNode

class mdp.nodes.IncrementalPCAScikitsLearnNode

Incremental principal components analysis (IPCA). This node has been automatically generated by wrapping the sklearn.decomposition.incremental_pca.IncrementalPCA class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Linear dimensionality reduction using Singular Value Decomposition of centered data, keeping only the most significant singular vectors to project the data to a lower dimensional space.

Depending on the size of the input data, this algorithm can be much more memory efficient than a PCA.

This algorithm has constant memory complexity, on the order of batch_size, enabling use of np.memmap files without loading the entire file into memory.

The computational overhead of each SVD is O(batch_size * n_features ** 2), but only 2 * batch_size samples remain in memory at a time. There will be n_samples / batch_size SVD computations to get the principal components, versus 1 large SVD of complexity O(n_samples * n_features ** 2) for PCA.

Read more in the User Guide.

Parameters

n_components : int or None, (default=None)
Number of components to keep. If n_components `` is ``None, then n_components is set to min(n_samples, n_features).
whiten : bool, optional

When True (False by default) the components_ vectors are divided by n_samples times components_ to ensure uncorrelated outputs with unit component-wise variances.

Whitening will remove some information from the transformed signal (the relative variance scales of the components) but can sometimes improve the predictive accuracy of the downstream estimators by making data respect some hard-wired assumptions.

copy : bool, (default=True)
If False, X will be overwritten. copy=False can be used to save memory but is unsafe for general use.
batch_size : int or None, (default=None)
The number of samples to use for each batch. Only used when calling fit. If batch_size is None, then batch_size is inferred from the data and set to 5 * n_features, to provide a balance between approximation accuracy and memory consumption.

Attributes

components_ : array, shape (n_components, n_features)
Components with maximum variance.
explained_variance_ : array, shape (n_components,)
Variance explained by each of the selected components.
explained_variance_ratio_ : array, shape (n_components,)
Percentage of variance explained by each of the selected components. If all components are stored, the sum of explained variances is equal to 1.0.
singular_values_ : array, shape (n_components,)
The singular values corresponding to each of the selected components. The singular values are equal to the 2-norms of the n_components variables in the lower-dimensional space.
mean_ : array, shape (n_features,)
Per-feature empirical mean, aggregate over calls to partial_fit.
var_ : array, shape (n_features,)
Per-feature empirical variance, aggregate over calls to partial_fit.
noise_variance_ : float
The estimated noise covariance following the Probabilistic PCA model from Tipping and Bishop 1999. See “Pattern Recognition and Machine Learning” by C. Bishop, 12.2.1 p. 574 or http://www.miketipping.com/papers/met-mppca.pdf.
n_components_ : int
The estimated number of components. Relevant when n_components=None.
n_samples_seen_ : int
The number of samples processed by the estimator. Will be reset on new calls to fit, but increments across partial_fit calls.

Examples

>>> from sklearn.datasets import load_digits
>>> from sklearn.decomposition import IncrementalPCA
>>> X, _ = load_digits(return_X_y=True)
>>> transformer = IncrementalPCA(n_components=7, batch_size=200)
>>> # either partially fit on smaller batches of data
>>> transformer.partial_fit(X[:100, :])
IncrementalPCA(batch_size=200, copy=True, n_components=7, whiten=False)
>>> # or let the fit function itself divide the data into batches
>>> X_transformed = transformer.fit_transform(X)
>>> X_transformed.shape
(1797, 7)

Notes

Implements the incremental PCA model from:

D. Ross, J. Lim, R. Lin, M. Yang, Incremental Learning for Robust Visual Tracking, International Journal of Computer Vision, Volume 77, Issue 1-3, pp. 125-141, May 2008. See http://www.cs.toronto.edu/~dross/ivt/RossLimLinYang_ijcv.pdf

This model is an extension of the Sequential Karhunen-Loeve Transform from:

A. Levy and M. Lindenbaum, Sequential Karhunen-Loeve Basis Extraction and its Application to Images, IEEE Transactions on Image Processing, Volume 9, Number 8, pp. 1371-1374, August 2000. See http://www.cs.technion.ac.il/~mic/doc/skl-ip.pdf

We have specifically abstained from an optimization used by authors of both papers, a QR decomposition used in specific situations to reduce the algorithmic complexity of the SVD. The source for this technique is Matrix Computations, Third Edition, G. Holub and C. Van Loan, Chapter 5, section 5.4.4, pp 252-253.. This technique has been omitted because it is advantageous only when decomposing a matrix with n_samples (rows) >= 5/3 * n_features (columns), and hurts the readability of the implemented algorithm. This would be a good opportunity for future optimization, if it is deemed necessary.

References

  1. Ross, J. Lim, R. Lin, M. Yang. Incremental Learning for Robust Visual
    Tracking, International Journal of Computer Vision, Volume 77, Issue 1-3, pp. 125-141, May 2008.
  1. Golub and C. Van Loan. Matrix Computations, Third Edition, Chapter 5,
    Section 5.4.4, pp. 252-253.

See also

PCA KernelPCA SparsePCA TruncatedSVD

Full API documentation: IncrementalPCAScikitsLearnNode

class mdp.nodes.MiniBatchSparsePCAScikitsLearnNode

Mini-batch Sparse Principal Components Analysis This node has been automatically generated by wrapping the sklearn.decomposition.sparse_pca.MiniBatchSparsePCA class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Finds the set of sparse components that can optimally reconstruct the data. The amount of sparseness is controllable by the coefficient of the L1 penalty, given by the parameter alpha.

Read more in the User Guide.

Parameters

n_components : int,
number of sparse atoms to extract
alpha : int,
Sparsity controlling parameter. Higher values lead to sparser components.
ridge_alpha : float,
Amount of ridge shrinkage to apply in order to improve conditioning when calling the transform method.
n_iter : int,
number of iterations to perform for each mini batch
callback : callable or None, optional (default: None)
callable that gets invoked every five iterations
batch_size : int,
the number of features to take in each mini batch
verbose : int
Controls the verbosity; the higher, the more messages. Defaults to 0.
shuffle : boolean,
whether to shuffle the data before splitting it in batches
n_jobs : int or None, optional (default=None)
Number of parallel jobs to run. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
method : {‘lars’, ‘cd’}
lars: uses the least angle regression method to solve the lasso problem (linear_model.lars_path) cd: uses the coordinate descent method to compute the Lasso solution (linear_model.Lasso). Lars will be faster if the estimated components are sparse.
random_state : int, RandomState instance or None, optional (default=None)
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.
normalize_components : boolean, optional (default=False)
  • if False, use a version of Sparse PCA without components normalization and without data centering. This is likely a bug and even though it’s the default for backward compatibility, this should not be used.
  • if True, use a version of Sparse PCA with components normalization and data centering.

New in version 0.20.

Deprecated since version 0.22: normalize_components was added and set to False for backward compatibility. It would be set to True from 0.22 onwards.

Attributes

components_ : array, [n_components, n_features]
Sparse components extracted from the data.
n_iter_ : int
Number of iterations run.
mean_ : array, shape (n_features,)
Per-feature empirical mean, estimated from the training set. Equal to X.mean(axis=0).

Examples

>>> import numpy as np
>>> from sklearn.datasets import make_friedman1
>>> from sklearn.decomposition import MiniBatchSparsePCA
>>> X, _ = make_friedman1(n_samples=200, n_features=30, random_state=0)
>>> transformer = MiniBatchSparsePCA(n_components=5,
...         batch_size=50,
...         normalize_components=True,
...         random_state=0)
>>> transformer.fit(X) 
MiniBatchSparsePCA(...)
>>> X_transformed = transformer.transform(X)
>>> X_transformed.shape
(200, 5)
>>> # most values in the ``components_`` are zero (sparsity)
>>> np.mean(transformer.components_ == 0)
0.94

See also

PCA SparsePCA DictionaryLearning

Full API documentation: MiniBatchSparsePCAScikitsLearnNode

class mdp.nodes.FactorAnalysisScikitsLearnNode

Factor Analysis (FA) This node has been automatically generated by wrapping the sklearn.decomposition.factor_analysis.FactorAnalysis class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. A simple linear generative model with Gaussian latent variables.

The observations are assumed to be caused by a linear transformation of lower dimensional latent factors and added Gaussian noise. Without loss of generality the factors are distributed according to a Gaussian with zero mean and unit covariance. The noise is also zero mean and has an arbitrary diagonal covariance matrix.

If we would restrict the model further, by assuming that the Gaussian noise is even isotropic (all diagonal entries are the same) we would obtain PPCA.

FactorAnalysis performs a maximum likelihood estimate of the so-called loading matrix, the transformation of the latent variables to the observed ones, using expectation-maximization (EM).

Read more in the User Guide.

Parameters

n_components : int | None
Dimensionality of latent space, the number of components of X that are obtained after transform. If None, n_components is set to the number of features.
tol : float
Stopping tolerance for EM algorithm.
copy : bool
Whether to make a copy of X. If False, the input X gets overwritten during fitting.
max_iter : int
Maximum number of iterations.
noise_variance_init : None | array, shape=(n_features,)
The initial guess of the noise variance for each feature. If None, it defaults to np.ones(n_features)
svd_method : {‘lapack’, ‘randomized’}
Which SVD method to use. If ‘lapack’ use standard SVD from scipy.linalg, if ‘randomized’ use fast randomized_svd function. Defaults to ‘randomized’. For most applications ‘randomized’ will be sufficiently precise while providing significant speed gains. Accuracy can also be improved by setting higher values for iterated_power. If this is not sufficient, for maximum precision you should choose ‘lapack’.
iterated_power : int, optional
Number of iterations for the power method. 3 by default. Only used if svd_method equals ‘randomized’
random_state : int, RandomState instance or None, optional (default=0)
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random. Only used when svd_method equals ‘randomized’.

Attributes

components_ : array, [n_components, n_features]
Components with maximum variance.
loglike_ : list, [n_iterations]
The log likelihood at each iteration.
noise_variance_ : array, shape=(n_features,)
The estimated noise variance for each feature.
n_iter_ : int
Number of iterations run.

Examples

>>> from sklearn.datasets import load_digits
>>> from sklearn.decomposition import FactorAnalysis
>>> X, _ = load_digits(return_X_y=True)
>>> transformer = FactorAnalysis(n_components=7, random_state=0)
>>> X_transformed = transformer.fit_transform(X)
>>> X_transformed.shape
(1797, 7)

References

See also

PCA: Principal component analysis is also a latent linear variable model
which however assumes equal noise variance for each feature. This extra assumption makes probabilistic PCA faster as it can be computed in closed form.
FastICA: Independent component analysis, a latent variable model with
non-Gaussian latent variables.

Full API documentation: FactorAnalysisScikitsLearnNode

class mdp.nodes.FunctionTransformerScikitsLearnNode

Constructs a transformer from an arbitrary callable. This node has been automatically generated by wrapping the sklearn.preprocessing._function_transformer.FunctionTransformer class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. A FunctionTransformer forwards its X (and optionally y) arguments to a user-defined function or function object and returns the result of this function. This is useful for stateless transformations such as taking the log of frequencies, doing custom scaling, etc.

Note: If a lambda is used as the function, then the resulting transformer will not be pickleable.

New in version 0.17.

Read more in the User Guide.

Parameters

func : callable, optional default=None
The callable to use for the transformation. This will be passed the same arguments as transform, with args and kwargs forwarded. If func is None, then func will be the identity function.
inverse_func : callable, optional default=None
The callable to use for the inverse transformation. This will be passed the same arguments as inverse transform, with args and kwargs forwarded. If inverse_func is None, then inverse_func will be the identity function.
validate : bool, optional default=True

Indicate that the input X array should be checked before calling func. The possibilities are:

  • If False, there is no input validation.
  • If True, then X will be converted to a 2-dimensional NumPy array or sparse matrix. If the conversion is not possible an exception is raised.

Deprecated since version 0.20: validate=True as default will be replaced by validate=False in 0.22.

accept_sparse : boolean, optional
Indicate that func accepts a sparse matrix as input. If validate is False, this has no effect. Otherwise, if accept_sparse is false, sparse matrix inputs will cause an exception to be raised.
pass_y : bool, optional default=False
Indicate that transform should forward the y argument to the inner callable.
check_inverse : bool, default=True

Whether to check that or func followed by inverse_func leads to the original inputs. It can be used for a sanity check, raising a warning when the condition is not fulfilled.

New in version 0.20.

kw_args : dict, optional
Dictionary of additional keyword arguments to pass to func.
inv_kw_args : dict, optional
Dictionary of additional keyword arguments to pass to inverse_func.

Full API documentation: FunctionTransformerScikitsLearnNode

class mdp.nodes.LassoLarsICScikitsLearnNode

Lasso model fit with Lars using BIC or AIC for model selection This node has been automatically generated by wrapping the sklearn.linear_model.least_angle.LassoLarsIC class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. The optimization objective for Lasso is:

(1 / (2 * n_samples)) * ||y - Xw||^2_2 + alpha * ||w||_1

AIC is the Akaike information criterion and BIC is the Bayes Information criterion. Such criteria are useful to select the value of the regularization parameter by making a trade-off between the goodness of fit and the complexity of the model. A good model should explain well the data while being simple.

Read more in the User Guide.

Parameters

criterion : ‘bic’ | ‘aic’
The type of criterion to use.
fit_intercept : boolean
whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (e.g. data is expected to be already centered).
verbose : boolean or integer, optional
Sets the verbosity amount
normalize : boolean, optional, default True
This parameter is ignored when fit_intercept is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use sklearn.preprocessing.StandardScaler before calling fit on an estimator with normalize=False.
precompute : True | False | ‘auto’ | array-like
Whether to use a precomputed Gram matrix to speed up calculations. If set to 'auto' let us decide. The Gram matrix can also be passed as argument.
max_iter : integer, optional
Maximum number of iterations to perform. Can be used for early stopping.
eps : float, optional
The machine-precision regularization in the computation of the Cholesky diagonal factors. Increase this for very ill-conditioned systems. Unlike the tol parameter in some iterative optimization-based algorithms, this parameter does not control the tolerance of the optimization.
copy_X : boolean, optional, default True
If True, X will be copied; else, it may be overwritten.
positive : boolean (default=False)
Restrict coefficients to be >= 0. Be aware that you might want to remove fit_intercept which is set True by default. Under the positive restriction the model coefficients do not converge to the ordinary-least-squares solution for small values of alpha. Only coefficients up to the smallest alpha value (alphas_[alphas_ > 0.].min() when fit_path=True) reached by the stepwise Lars-Lasso algorithm are typically in congruence with the solution of the coordinate descent Lasso estimator. As a consequence using LassoLarsIC only makes sense for problems where a sparse solution is expected and/or reached.

Attributes

coef_ : array, shape (n_features,)
parameter vector (w in the formulation formula)
intercept_ : float
independent term in decision function.
alpha_ : float
the alpha parameter chosen by the information criterion
n_iter_ : int
number of iterations run by lars_path to find the grid of alphas.
criterion_ : array, shape (n_alphas,)
The value of the information criteria (‘aic’, ‘bic’) across all alphas. The alpha which has the smallest information criterion is chosen. This value is larger by a factor of n_samples compared to Eqns. 2.15 and 2.16 in (Zou et al, 2007).

Examples

>>> from sklearn import linear_model
>>> reg = linear_model.LassoLarsIC(criterion='bic')
>>> reg.fit([[-1, 1], [0, 0], [1, 1]], [-1.1111, 0, -1.1111])
... 
LassoLarsIC(copy_X=True, criterion='bic', eps=..., fit_intercept=True,
      max_iter=500, normalize=True, positive=False, precompute='auto',
      verbose=False)
>>> print(reg.coef_) 
[ 0.  -1.11...]

Notes

The estimation of the number of degrees of freedom is given by:

“On the degrees of freedom of the lasso” Hui Zou, Trevor Hastie, and Robert Tibshirani Ann. Statist. Volume 35, Number 5 (2007), 2173-2192.

https://en.wikipedia.org/wiki/Akaike_information_criterion https://en.wikipedia.org/wiki/Bayesian_information_criterion

See also

lars_path, LassoLars, LassoLarsCV

Full API documentation: LassoLarsICScikitsLearnNode

class mdp.nodes.RFEScikitsLearnNode

Feature ranking with recursive feature elimination. This node has been automatically generated by wrapping the sklearn.feature_selection.rfe.RFE class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Given an external estimator that assigns weights to features (e.g., the coefficients of a linear model), the goal of recursive feature elimination (RFE) is to select features by recursively considering smaller and smaller sets of features. First, the estimator is trained on the initial set of features and the importance of each feature is obtained either through a coef_ attribute or through a feature_importances_ attribute. Then, the least important features are pruned from current set of features. That procedure is recursively repeated on the pruned set until the desired number of features to select is eventually reached.

Read more in the User Guide.

Parameters

estimator : object
A supervised learning estimator with a fit method that provides information about feature importance either through a coef_ attribute or through a feature_importances_ attribute.
n_features_to_select : int or None (default=None)
The number of features to select. If None, half of the features are selected.
step : int or float, optional (default=1)
If greater than or equal to 1, then step corresponds to the (integer) number of features to remove at each iteration. If within (0.0, 1.0), then step corresponds to the percentage (rounded down) of features to remove at each iteration.
verbose : int, (default=0)
Controls verbosity of output.

Attributes

n_features_ : int
The number of selected features.
support_ : array of shape [n_features]
The mask of selected features.
ranking_ : array of shape [n_features]
The feature ranking, such that ranking_[i] corresponds to the ranking position of the i-th feature. Selected (i.e., estimated best) features are assigned rank 1.
estimator_ : object
The external estimator fit on the reduced dataset.

Examples

The following example shows how to retrieve the 5 right informative features in the Friedman #1 dataset.

>>> from sklearn.datasets import make_friedman1
>>> from sklearn.feature_selection import RFE
>>> from sklearn.svm import SVR
>>> X, y = make_friedman1(n_samples=50, n_features=10, random_state=0)
>>> estimator = SVR(kernel="linear")
>>> selector = RFE(estimator, 5, step=1)
>>> selector = selector.fit(X, y)
>>> selector.support_ 
array([ True,  True,  True,  True,  True, False, False, False, False,
       False])
>>> selector.ranking_
array([1, 1, 1, 1, 1, 6, 4, 3, 2, 5])

See also

RFECV : Recursive feature elimination with built-in cross-validated
selection of the best number of features

References

[1]Guyon, I., Weston, J., Barnhill, S., & Vapnik, V., “Gene selection for cancer classification using support vector machines”, Mach. Learn., 46(1-3), 389–422, 2002.

Full API documentation: RFEScikitsLearnNode

class mdp.nodes.PCAScikitsLearnNode

Principal component analysis (PCA) This node has been automatically generated by wrapping the sklearn.decomposition.pca.PCA class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Linear dimensionality reduction using Singular Value Decomposition of the data to project it to a lower dimensional space.

It uses the LAPACK implementation of the full SVD or a randomized truncated SVD by the method of Halko et al. 2009, depending on the shape of the input data and the number of components to extract.

It can also use the scipy.sparse.linalg ARPACK implementation of the truncated SVD.

Notice that this class does not support sparse input. See TruncatedSVD for an alternative with sparse data.

Read more in the User Guide.

Parameters

n_components : int, float, None or string

Number of components to keep. if n_components is not set all components are kept:

n_components == min(n_samples, n_features)

If n_components == 'mle' and svd_solver == 'full', Minka’s MLE is used to guess the dimension. Use of n_components == 'mle' will interpret svd_solver == 'auto' as svd_solver == 'full'.

If 0 < n_components < 1 and svd_solver == 'full', select the number of components such that the amount of variance that needs to be explained is greater than the percentage specified by n_components.

If svd_solver == 'arpack', the number of components must be strictly less than the minimum of n_features and n_samples.

Hence, the None case results in:

n_components == min(n_samples, n_features) - 1
copy : bool (default True)
If False, data passed to fit are overwritten and running fit(X).transform(X) will not yield the expected results, use fit_transform(X) instead.
whiten : bool, optional (default False)

When True (False by default) the components_ vectors are multiplied by the square root of n_samples and then divided by the singular values to ensure uncorrelated outputs with unit component-wise variances.

Whitening will remove some information from the transformed signal (the relative variance scales of the components) but can sometime improve the predictive accuracy of the downstream estimators by making their data respect some hard-wired assumptions.

svd_solver : string {‘auto’, ‘full’, ‘arpack’, ‘randomized’}

auto :

  • the solver is selected by a default policy based on X.shape and
  • n_components: if the input data is larger than 500x500 and the
  • number of components to extract is lower than 80% of the smallest
  • dimension of the data, then the more efficient ‘randomized’
  • method is enabled. Otherwise the exact full SVD is computed and
  • optionally truncated afterwards.

full :

  • run exact full SVD calling the standard LAPACK solver via
  • scipy.linalg.svd and select the components by postprocessing

arpack :

  • run SVD truncated to n_components calling ARPACK solver via
  • scipy.sparse.linalg.svds. It requires strictly
  • 0 < n_components < min(X.shape)

randomized :

  • run randomized SVD by the method of Halko et al.

New in version 0.18.0.

tol : float >= 0, optional (default .0)

Tolerance for singular values computed by svd_solver == ‘arpack’.

New in version 0.18.0.

iterated_power : int >= 0, or ‘auto’, (default ‘auto’)

Number of iterations for the power method computed by svd_solver == ‘randomized’.

New in version 0.18.0.

random_state : int, RandomState instance or None, optional (default None)

If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random. Used when svd_solver == ‘arpack’ or ‘randomized’.

New in version 0.18.0.

Attributes

components_ : array, shape (n_components, n_features)
Principal axes in feature space, representing the directions of maximum variance in the data. The components are sorted by explained_variance_.
explained_variance_ : array, shape (n_components,)

The amount of variance explained by each of the selected components.

Equal to n_components largest eigenvalues of the covariance matrix of X.

New in version 0.18.

explained_variance_ratio_ : array, shape (n_components,)

Percentage of variance explained by each of the selected components.

If n_components is not set then all components are stored and the sum of the ratios is equal to 1.0.

singular_values_ : array, shape (n_components,)
The singular values corresponding to each of the selected components. The singular values are equal to the 2-norms of the n_components variables in the lower-dimensional space.
mean_ : array, shape (n_features,)

Per-feature empirical mean, estimated from the training set.

Equal to X.mean(axis=0).

n_components_ : int
The estimated number of components. When n_components is set to ‘mle’ or a number between 0 and 1 (with svd_solver == ‘full’) this number is estimated from input data. Otherwise it equals the parameter n_components, or the lesser value of n_features and n_samples if n_components is None.
noise_variance_ : float

The estimated noise covariance following the Probabilistic PCA model from Tipping and Bishop 1999. See “Pattern Recognition and Machine Learning” by C. Bishop, 12.2.1 p. 574 or http://www.miketipping.com/papers/met-mppca.pdf. It is required to compute the estimated data covariance and score samples.

Equal to the average of (min(n_features, n_samples) - n_components) smallest eigenvalues of the covariance matrix of X.

References

For n_components == ‘mle’, this class uses the method of Minka, T. P. “Automatic choice of dimensionality for PCA”. In NIPS, pp. 598-604

Implements the probabilistic PCA model from:

`Tipping, M. E., and Bishop, C. M. (1999). “Probabilistic principal component analysis”. Journal of the Royal Statistical Society:

Series B (Statistical Methodology), 61(3), 611-622. via the score and score_samples methods. See http://www.miketipping.com/papers/met-mppca.pdf

For svd_solver == ‘arpack’, refer to scipy.sparse.linalg.svds.

For svd_solver == ‘randomized’, see:

Halko, N., Martinsson, P. G., and Tropp, J. A. (2011). “Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions”. SIAM review, 53(2), 217-288. and also Martinsson, P. G., Rokhlin, V., and Tygert, M. (2011). “A randomized algorithm for the decomposition of matrices”. Applied and Computational Harmonic Analysis, 30(1), 47-68.

Examples

>>> import numpy as np
>>> from sklearn.decomposition import PCA
>>> X = np.array([[-1, -1], [-2, -1], [-3, -2], [1, 1], [2, 1], [3, 2]])
>>> pca = PCA(n_components=2)
>>> pca.fit(X)
PCA(copy=True, iterated_power='auto', n_components=2, random_state=None,
  svd_solver='auto', tol=0.0, whiten=False)
>>> print(pca.explained_variance_ratio_)  
[0.9924... 0.0075...]
>>> print(pca.singular_values_)  
[6.30061... 0.54980...]
>>> pca = PCA(n_components=2, svd_solver='full')
>>> pca.fit(X)                 
PCA(copy=True, iterated_power='auto', n_components=2, random_state=None,
  svd_solver='full', tol=0.0, whiten=False)
>>> print(pca.explained_variance_ratio_)  
[0.9924... 0.00755...]
>>> print(pca.singular_values_)  
[6.30061... 0.54980...]
>>> pca = PCA(n_components=1, svd_solver='arpack')
>>> pca.fit(X)
PCA(copy=True, iterated_power='auto', n_components=1, random_state=None,
  svd_solver='arpack', tol=0.0, whiten=False)
>>> print(pca.explained_variance_ratio_)  
[0.99244...]
>>> print(pca.singular_values_)  
[6.30061...]

See also

KernelPCA SparsePCA TruncatedSVD IncrementalPCA

Full API documentation: PCAScikitsLearnNode

class mdp.nodes.MultiTaskLassoScikitsLearnNode

Multi-task Lasso model trained with L1/L2 mixed-norm as regularizer. This node has been automatically generated by wrapping the sklearn.linear_model.coordinate_descent.MultiTaskLasso class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. The optimization objective for Lasso is:

(1 / (2 * n_samples)) * ||Y - XW||^2_Fro + alpha * ||W||_21

Where:

||W||_21 = \sum_i \sqrt{\sum_j w_{ij}^2}

i.e. the sum of norm of each row.

Read more in the User Guide.

Parameters

alpha : float, optional
Constant that multiplies the L1/L2 term. Defaults to 1.0
fit_intercept : boolean
whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (e.g. data is expected to be already centered).
normalize : boolean, optional, default False
This parameter is ignored when fit_intercept is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use sklearn.preprocessing.StandardScaler before calling fit on an estimator with normalize=False.
copy_X : boolean, optional, default True
If True, X will be copied; else, it may be overwritten.
max_iter : int, optional
The maximum number of iterations
tol : float, optional
The tolerance for the optimization: if the updates are smaller than tol, the optimization code checks the dual gap for optimality and continues until it is smaller than tol.
warm_start : bool, optional
When set to True, reuse the solution of the previous call to fit as initialization, otherwise, just erase the previous solution. See the Glossary.
random_state : int, RandomState instance or None, optional, default None
The seed of the pseudo random number generator that selects a random feature to update. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random. Used when selection == ‘random’.
selection : str, default ‘cyclic’
If set to ‘random’, a random coefficient is updated every iteration rather than looping over features sequentially by default. This (setting to ‘random’) often leads to significantly faster convergence especially when tol is higher than 1e-4

Attributes

coef_ : array, shape (n_tasks, n_features)
Parameter vector (W in the cost function formula). Note that coef_ stores the transpose of W, W.T.
intercept_ : array, shape (n_tasks,)
independent term in decision function.
n_iter_ : int
number of iterations run by the coordinate descent solver to reach the specified tolerance.

Examples

>>> from sklearn import linear_model
>>> clf = linear_model.MultiTaskLasso(alpha=0.1)
>>> clf.fit([[0,0], [1, 1], [2, 2]], [[0, 0], [1, 1], [2, 2]])
MultiTaskLasso(alpha=0.1, copy_X=True, fit_intercept=True, max_iter=1000,
        normalize=False, random_state=None, selection='cyclic', tol=0.0001,
        warm_start=False)
>>> print(clf.coef_)
[[0.89393398 0.        ]
 [0.89393398 0.        ]]
>>> print(clf.intercept_)
[0.10606602 0.10606602]

See also

MultiTaskLasso : Multi-task L1/L2 Lasso with built-in cross-validation Lasso MultiTaskElasticNet

Notes

The algorithm used to fit the model is coordinate descent.

To avoid unnecessary memory duplication the X argument of the fit method should be directly passed as a Fortran-contiguous numpy array.

Full API documentation: MultiTaskLassoScikitsLearnNode

class mdp.nodes.RandomizedLogisticRegressionScikitsLearnNode

Randomized Logistic Regression This node has been automatically generated by wrapping the sklearn.linear_model.randomized_l1.RandomizedLogisticRegression class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Randomized Logistic Regression works by subsampling the training data and fitting a L1-penalized LogisticRegression model where the penalty of a random subset of coefficients has been scaled. By performing this double randomization several times, the method assigns high scores to features that are repeatedly selected across randomizations. This is known as stability selection. In short, features selected more often are considered good features.

Parameters

C : float or array-like of shape [n_reg_parameter], optional, default=1
The regularization parameter C in the LogisticRegression. When C is an array, fit will take each regularization parameter in C one by one for LogisticRegression and store results for each one in all_scores_, where columns and rows represent corresponding reg_parameters and features.
scaling : float, optional, default=0.5
The s parameter used to randomly scale the penalty of different features. Should be between 0 and 1.
sample_fraction : float, optional, default=0.75
The fraction of samples to be used in each randomized design. Should be between 0 and 1. If 1, all samples are used.
n_resampling : int, optional, default=200
Number of randomized models.
selection_threshold : float, optional, default=0.25
The score above which features should be selected.
tol : float, optional, default=1e-3
tolerance for stopping criteria of LogisticRegression
fit_intercept : boolean, optional, default=True
whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (e.g. data is expected to be already centered).
verbose : boolean or integer, optional
Sets the verbosity amount
normalize : boolean, optional, default True
If True, the regressors X will be normalized before regression. This parameter is ignored when fit_intercept is set to False. When the regressors are normalized, note that this makes the hyperparameters learnt more robust and almost independent of the number of samples. The same property is not valid for standardized data. However, if you wish to standardize, please use preprocessing.StandardScaler before calling fit on an estimator with normalize=False.
random_state : int, RandomState instance or None, optional (default=None)
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.
n_jobs : int or None, optional (default=None)
Number of CPUs to use during the resampling. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
pre_dispatch : int, or string, optional

Controls the number of jobs that get dispatched during parallel execution. Reducing this number can be useful to avoid an explosion of memory consumption when more jobs get dispatched than CPUs can process. This parameter can be:

  • None, in which case all the jobs are immediately created and spawned. Use this for lightweight and fast-running jobs, to avoid delays due to on-demand spawning of the jobs
  • An int, giving the exact number of total jobs that are spawned
  • A string, giving an expression as a function of n_jobs, as in ‘2*n_jobs’
memory : None, str or object with the joblib.Memory interface, optional (default=None)
Used for internal caching. By default, no caching is done. If a string is given, it is the path to the caching directory.

Attributes

scores_ : array, shape = [n_features]
Feature scores between 0 and 1.
all_scores_ : array, shape = [n_features, n_reg_parameter]
Feature scores between 0 and 1 for all values of the regularization parameter. The reference article suggests scores_ is the max of all_scores_.

Examples

>>> from sklearn.linear_model import RandomizedLogisticRegression
>>> randomized_logistic = RandomizedLogisticRegression() 

References

Stability selection Nicolai Meinshausen, Peter Buhlmann Journal of the Royal Statistical Society: Series B Volume 72, Issue 4, pages 417-473, September 2010 DOI: 10.1111/j.1467-9868.2010.00740.x

See also

RandomizedLasso, LogisticRegression

Full API documentation: RandomizedLogisticRegressionScikitsLearnNode

class mdp.nodes.SelectFweScikitsLearnNode

Filter: Select the p-values corresponding to Family-wise error rate This node has been automatically generated by wrapping the sklearn.feature_selection.univariate_selection.SelectFwe class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Read more in the User Guide.

Parameters

score_func : callable
Function taking two arrays X and y, and returning a pair of arrays (scores, pvalues). Default is f_classif (see below “See also”). The default function only works with classification tasks.
alpha : float, optional
The highest uncorrected p-value for features to keep.

Examples

>>> from sklearn.datasets import load_breast_cancer
>>> from sklearn.feature_selection import SelectFwe, chi2
>>> X, y = load_breast_cancer(return_X_y=True)
>>> X.shape
(569, 30)
>>> X_new = SelectFwe(chi2, alpha=0.01).fit_transform(X, y)
>>> X_new.shape
(569, 15)

Attributes

scores_ : array-like, shape=(n_features,)
Scores of features.
pvalues_ : array-like, shape=(n_features,)
p-values of feature scores.

See also

f_classif: ANOVA F-value between label/feature for classification tasks. chi2: Chi-squared stats of non-negative features for classification tasks. f_regression: F-value between label/feature for regression tasks. SelectPercentile: Select features based on percentile of the highest scores. SelectKBest: Select features based on the k highest scores. SelectFpr: Select features based on a false positive rate test. SelectFdr: Select features based on an estimated false discovery rate. GenericUnivariateSelect: Univariate feature selector with configurable mode.

Full API documentation: SelectFweScikitsLearnNode

class mdp.nodes.MultiTaskElasticNetScikitsLearnNode

Multi-task ElasticNet model trained with L1/L2 mixed-norm as regularizer This node has been automatically generated by wrapping the sklearn.linear_model.coordinate_descent.MultiTaskElasticNet class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. The optimization objective for MultiTaskElasticNet is:

(1 / (2 * n_samples)) * ||Y - XW||_Fro^2
+ alpha * l1_ratio * ||W||_21
+ 0.5 * alpha * (1 - l1_ratio) * ||W||_Fro^2

Where:

||W||_21 = sum_i sqrt(sum_j w_ij ^ 2)

i.e. the sum of norm of each row.

Read more in the User Guide.

Parameters

alpha : float, optional
Constant that multiplies the L1/L2 term. Defaults to 1.0
l1_ratio : float
The ElasticNet mixing parameter, with 0 < l1_ratio <= 1. For l1_ratio = 1 the penalty is an L1/L2 penalty. For l1_ratio = 0 it is an L2 penalty. For 0 < l1_ratio < 1, the penalty is a combination of L1/L2 and L2.
fit_intercept : boolean
whether to calculate the intercept for this model. If set to false, no intercept will be used in calculations (e.g. data is expected to be already centered).
normalize : boolean, optional, default False
This parameter is ignored when fit_intercept is set to False. If True, the regressors X will be normalized before regression by subtracting the mean and dividing by the l2-norm. If you wish to standardize, please use sklearn.preprocessing.StandardScaler before calling fit on an estimator with normalize=False.
copy_X : boolean, optional, default True
If True, X will be copied; else, it may be overwritten.
max_iter : int, optional
The maximum number of iterations
tol : float, optional
The tolerance for the optimization: if the updates are smaller than tol, the optimization code checks the dual gap for optimality and continues until it is smaller than tol.
warm_start : bool, optional
When set to True, reuse the solution of the previous call to fit as initialization, otherwise, just erase the previous solution. See the Glossary.
random_state : int, RandomState instance or None, optional, default None
The seed of the pseudo random number generator that selects a random feature to update. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random. Used when selection == ‘random’.
selection : str, default ‘cyclic’
If set to ‘random’, a random coefficient is updated every iteration rather than looping over features sequentially by default. This (setting to ‘random’) often leads to significantly faster convergence especially when tol is higher than 1e-4.

Attributes

intercept_ : array, shape (n_tasks,)
Independent term in decision function.
coef_ : array, shape (n_tasks, n_features)
Parameter vector (W in the cost function formula). If a 1D y is passed in at fit (non multi-task usage), coef_ is then a 1D array. Note that coef_ stores the transpose of W, W.T.
n_iter_ : int
number of iterations run by the coordinate descent solver to reach the specified tolerance.

Examples

>>> from sklearn import linear_model
>>> clf = linear_model.MultiTaskElasticNet(alpha=0.1)
>>> clf.fit([[0,0], [1, 1], [2, 2]], [[0, 0], [1, 1], [2, 2]])
... 
MultiTaskElasticNet(alpha=0.1, copy_X=True, fit_intercept=True,
        l1_ratio=0.5, max_iter=1000, normalize=False, random_state=None,
        selection='cyclic', tol=0.0001, warm_start=False)
>>> print(clf.coef_)
[[0.45663524 0.45612256]
 [0.45663524 0.45612256]]
>>> print(clf.intercept_)
[0.0872422 0.0872422]

See also

MultiTaskElasticNet : Multi-task L1/L2 ElasticNet with built-in
cross-validation.

ElasticNet MultiTaskLasso

Notes

The algorithm used to fit the model is coordinate descent.

To avoid unnecessary memory duplication the X argument of the fit method should be directly passed as a Fortran-contiguous numpy array.

Full API documentation: MultiTaskElasticNetScikitsLearnNode

class mdp.nodes.SparseCoderScikitsLearnNode

Sparse coding This node has been automatically generated by wrapping the sklearn.decomposition.dict_learning.SparseCoder class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Finds a sparse representation of data against a fixed, precomputed dictionary.

Each row of the result is the solution to a sparse coding problem. The goal is to find a sparse array code such that:

X ~= code * dictionary

Read more in the User Guide.

Parameters

dictionary : array, [n_components, n_features]
The dictionary atoms used for sparse coding. Lines are assumed to be normalized to unit norm.
transform_algorithm : {‘lasso_lars’, ‘lasso_cd’, ‘lars’, ‘omp’, ‘threshold’}

Algorithm used to transform the data:

  • lars: uses the least angle regression method (linear_model.lars_path)
  • lasso_lars: uses Lars to compute the Lasso solution
  • lasso_cd: uses the coordinate descent method to compute the
  • Lasso solution (linear_model.Lasso). lasso_lars will be faster if
  • the estimated components are sparse.
  • omp: uses orthogonal matching pursuit to estimate the sparse solution
  • threshold: squashes to zero all coefficients less than alpha from
  • the projection dictionary * X'
transform_n_nonzero_coefs : int, 0.1 * n_features by default
Number of nonzero coefficients to target in each column of the solution. This is only used by algorithm=’lars’ and algorithm=’omp’ and is overridden by alpha in the omp case.
transform_alpha : float, 1. by default
If algorithm=’lasso_lars’ or algorithm=’lasso_cd’, alpha is the penalty applied to the L1 norm. If algorithm=’threshold’, alpha is the absolute value of the threshold below which coefficients will be squashed to zero. If algorithm=’omp’, alpha is the tolerance parameter: the value of the reconstruction error targeted. In this case, it overrides n_nonzero_coefs.
split_sign : bool, False by default
Whether to split the sparse feature vector into the concatenation of its negative part and its positive part. This can improve the performance of downstream classifiers.
n_jobs : int or None, optional (default=None)
Number of parallel jobs to run. None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.
positive_code : bool

Whether to enforce positivity when finding the code.

New in version 0.20.

Attributes

components_ : array, [n_components, n_features]
The unchanged dictionary atoms

See also

DictionaryLearning MiniBatchDictionaryLearning SparsePCA MiniBatchSparsePCA sparse_encode

Full API documentation: SparseCoderScikitsLearnNode

class mdp.nodes.StandardScalerScikitsLearnNode

Standardize features by removing the mean and scaling to unit variance This node has been automatically generated by wrapping the sklearn.preprocessing.data.StandardScaler class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. The standard score of a sample x is calculated as:

z = (x - u) / s

where u is the mean of the training samples or zero if with_mean=False, and s is the standard deviation of the training samples or one if with_std=False.

Centering and scaling happen independently on each feature by computing the relevant statistics on the samples in the training set. Mean and standard deviation are then stored to be used on later data using the transform method.

Standardization of a dataset is a common requirement for many machine learning estimators: they might behave badly if the individual features do not more or less look like standard normally distributed data (e.g. Gaussian with 0 mean and unit variance).

For instance many elements used in the objective function of a learning algorithm (such as the RBF kernel of Support Vector Machines or the L1 and L2 regularizers of linear models) assume that all features are centered around 0 and have variance in the same order. If a feature has a variance that is orders of magnitude larger that others, it might dominate the objective function and make the estimator unable to learn from other features correctly as expected.

This scaler can also be applied to sparse CSR or CSC matrices by passing with_mean=False to avoid breaking the sparsity structure of the data.

Read more in the User Guide.

Parameters

copy : boolean, optional, default True
If False, try to avoid a copy and do inplace scaling instead. This is not guaranteed to always work inplace; e.g. if the data is not a NumPy array or scipy.sparse CSR matrix, a copy may still be returned.
with_mean : boolean, True by default
If True, center the data before scaling. This does not work (and will raise an exception) when attempted on sparse matrices, because centering them entails building a dense matrix which in common use cases is likely to be too large to fit in memory.
with_std : boolean, True by default
If True, scale the data to unit variance (or equivalently, unit standard deviation).

Attributes

scale_ : ndarray or None, shape (n_features,)

Per feature relative scaling of the data. This is calculated using np.sqrt(var_). Equal to None when with_std=False.

New in version 0.17: scale_

mean_ : ndarray or None, shape (n_features,)
The mean value for each feature in the training set. Equal to None when with_mean=False.
var_ : ndarray or None, shape (n_features,)
The variance for each feature in the training set. Used to compute scale_. Equal to None when with_std=False.
n_samples_seen_ : int or array, shape (n_features,)
The number of samples processed by the estimator for each feature. If there are not missing samples, the n_samples_seen will be an integer, otherwise it will be an array. Will be reset on new calls to fit, but increments across partial_fit calls.

Examples

>>> from sklearn.preprocessing import StandardScaler
>>> data = [[0, 0], [0, 0], [1, 1], [1, 1]]
>>> scaler = StandardScaler()
>>> print(scaler.fit(data))
StandardScaler(copy=True, with_mean=True, with_std=True)
>>> print(scaler.mean_)
[0.5 0.5]
>>> print(scaler.transform(data))
[[-1. -1.]
 [-1. -1.]
 [ 1.  1.]
 [ 1.  1.]]
>>> print(scaler.transform([[2, 2]]))
[[3. 3.]]

See also

scale: Equivalent function without the estimator API.

sklearn.decomposition.PCA
Further removes the linear correlation across features with ‘whiten=True’.

Notes

NaNs are treated as missing values: disregarded in fit, and maintained in transform.

We use a biased estimator for the standard deviation, equivalent to numpy.std(x, ddof=0). Note that the choice of ddof is unlikely to affect model performance.

For a comparison of the different scalers, transformers, and normalizers, see examples/preprocessing/plot_all_scaling.py.

Full API documentation: StandardScalerScikitsLearnNode

class mdp.nodes.DecisionTreeClassifierScikitsLearnNode

A decision tree classifier. This node has been automatically generated by wrapping the sklearn.tree.tree.DecisionTreeClassifier class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Read more in the User Guide.

Parameters

criterion : string, optional (default=”gini”)
The function to measure the quality of a split. Supported criteria are “gini” for the Gini impurity and “entropy” for the information gain.
splitter : string, optional (default=”best”)
The strategy used to choose the split at each node. Supported strategies are “best” to choose the best split and “random” to choose the best random split.
max_depth : int or None, optional (default=None)
The maximum depth of the tree. If None, then nodes are expanded until all leaves are pure or until all leaves contain less than min_samples_split samples.
min_samples_split : int, float, optional (default=2)

The minimum number of samples required to split an internal node:

  • If int, then consider min_samples_split as the minimum number.
  • If float, then min_samples_split is a fraction and ceil(min_samples_split * n_samples) are the minimum number of samples for each split.

Changed in version 0.18: Added float values for fractions.

min_samples_leaf : int, float, optional (default=1)

The minimum number of samples required to be at a leaf node. A split point at any depth will only be considered if it leaves at least min_samples_leaf training samples in each of the left and right branches. This may have the effect of smoothing the model, especially in regression.

  • If int, then consider min_samples_leaf as the minimum number.
  • If float, then min_samples_leaf is a fraction and ceil(min_samples_leaf * n_samples) are the minimum number of samples for each node.

Changed in version 0.18: Added float values for fractions.

min_weight_fraction_leaf : float, optional (default=0.)
The minimum weighted fraction of the sum total of weights (of all the input samples) required to be at a leaf node. Samples have equal weight when sample_weight is not provided.
max_features : int, float, string or None, optional (default=None)

The number of features to consider when looking for the best split:

  • If int, then consider max_features features at each split.
  • If float, then max_features is a fraction and int(max_features * n_features) features are considered at each split.
  • If “auto”, then max_features=sqrt(n_features).
  • If “sqrt”, then max_features=sqrt(n_features).
  • If “log2”, then max_features=log2(n_features).
  • If None, then max_features=n_features.

Note: the search for a split does not stop until at least one valid partition of the node samples is found, even if it requires to effectively inspect more than max_features features.

random_state : int, RandomState instance or None, optional (default=None)
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.
max_leaf_nodes : int or None, optional (default=None)
Grow a tree with max_leaf_nodes in best-first fashion. Best nodes are defined as relative reduction in impurity. If None then unlimited number of leaf nodes.
min_impurity_decrease : float, optional (default=0.)

A node will be split if this split induces a decrease of the impurity greater than or equal to this value.

The weighted impurity decrease equation is the following:

N_t / N * (impurity - N_t_R / N_t * right_impurity
                    - N_t_L / N_t * left_impurity)

where N is the total number of samples, N_t is the number of samples at the current node, N_t_L is the number of samples in the left child, and N_t_R is the number of samples in the right child.

N, N_t, N_t_R and N_t_L all refer to the weighted sum, if sample_weight is passed.

New in version 0.19.

min_impurity_split : float, (default=1e-7)

Threshold for early stopping in tree growth. A node will split if its impurity is above the threshold, otherwise it is a leaf.

Deprecated since version 0.19: min_impurity_split has been deprecated in favor of min_impurity_decrease in 0.19. The default value of min_impurity_split will change from 1e-7 to 0 in 0.23 and it will be removed in 0.25. Use min_impurity_decrease instead.

class_weight : dict, list of dicts, “balanced” or None, default=None

Weights associated with classes in the form {class_label: weight}. If not given, all classes are supposed to have weight one. For multi-output problems, a list of dicts can be provided in the same order as the columns of y.

Note that for multioutput (including multilabel) weights should be defined for each class of every column in its own dict. For example, for four-class multilabel classification weights should be [{0: 1, 1: 1}, {0: 1, 1: 5}, {0: 1, 1: 1}, {0: 1, 1: 1}] instead of [{1:1}, {2:5}, {3:1}, {4:1}].

The “balanced” mode uses the values of y to automatically adjust weights inversely proportional to class frequencies in the input data as n_samples / (n_classes * np.bincount(y))

For multi-output, the weights of each column of y will be multiplied.

Note that these weights will be multiplied with sample_weight (passed through the fit method) if sample_weight is specified.

presort : bool, optional (default=False)
Whether to presort the data to speed up the finding of best splits in fitting. For the default settings of a decision tree on large datasets, setting this to true may slow down the training process. When using either a smaller dataset or a restricted depth, this may speed up the training.

Attributes

classes_ : array of shape = [n_classes] or a list of such arrays
The classes labels (single output problem), or a list of arrays of class labels (multi-output problem).
feature_importances_ : array of shape = [n_features]
The feature importances. The higher, the more important the feature. The importance of a feature is computed as the (normalized) total reduction of the criterion brought by that feature. It is also known as the Gini importance [4]_.
max_features_ : int,
The inferred value of max_features.
n_classes_ : int or list
The number of classes (for single output problems), or a list containing the number of classes for each output (for multi-output problems).
n_features_ : int
The number of features when fit is performed.
n_outputs_ : int
The number of outputs when fit is performed.
tree_ : Tree object
The underlying Tree object. Please refer to help(sklearn.tree._tree.Tree) for attributes of Tree object and sphx_glr_auto_examples_tree_plot_unveil_tree_structure.py for basic usage of these attributes.

Notes

The default values for the parameters controlling the size of the trees (e.g. max_depth, min_samples_leaf, etc.) lead to fully grown and unpruned trees which can potentially be very large on some data sets. To reduce memory consumption, the complexity and size of the trees should be controlled by setting those parameter values.

The features are always randomly permuted at each split. Therefore, the best found split may vary, even with the same training data and max_features=n_features, if the improvement of the criterion is identical for several splits enumerated during the search of the best split. To obtain a deterministic behaviour during fitting, random_state has to be fixed.

See also

DecisionTreeRegressor

References

[1]https://en.wikipedia.org/wiki/Decision_tree_learning
[2]L. Breiman, J. Friedman, R. Olshen, and C. Stone, “Classification and Regression Trees”, Wadsworth, Belmont, CA, 1984.
[3]T. Hastie, R. Tibshirani and J. Friedman. “Elements of Statistical Learning”, Springer, 2009.
[4]L. Breiman, and A. Cutler, “Random Forests”, https://www.stat.berkeley.edu/~breiman/RandomForests/cc_home.htm

Examples

>>> from sklearn.datasets import load_iris
>>> from sklearn.model_selection import cross_val_score
>>> from sklearn.tree import DecisionTreeClassifier
>>> clf = DecisionTreeClassifier(random_state=0)
>>> iris = load_iris()
>>> cross_val_score(clf, iris.data, iris.target, cv=10)
...                             
...
array([ 1.     ,  0.93...,  0.86...,  0.93...,  0.93...,
        0.93...,  0.93...,  1.     ,  0.93...,  1.      ])

Full API documentation: DecisionTreeClassifierScikitsLearnNode

class mdp.nodes.GenericUnivariateSelectScikitsLearnNode

Univariate feature selector with configurable strategy. This node has been automatically generated by wrapping the sklearn.feature_selection.univariate_selection.GenericUnivariateSelect class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Read more in the User Guide.

Parameters

score_func : callable
Function taking two arrays X and y, and returning a pair of arrays (scores, pvalues). For modes ‘percentile’ or ‘kbest’ it can return a single array scores.
mode : {‘percentile’, ‘k_best’, ‘fpr’, ‘fdr’, ‘fwe’}
Feature selection mode.
param : float or int depending on the feature selection mode
Parameter of the corresponding mode.

Attributes

scores_ : array-like, shape=(n_features,)
Scores of features.
pvalues_ : array-like, shape=(n_features,)
p-values of feature scores, None if score_func returned scores only.

Examples

>>> from sklearn.datasets import load_breast_cancer
>>> from sklearn.feature_selection import GenericUnivariateSelect, chi2
>>> X, y = load_breast_cancer(return_X_y=True)
>>> X.shape
(569, 30)
>>> transformer = GenericUnivariateSelect(chi2, 'k_best', param=20)
>>> X_new = transformer.fit_transform(X, y)
>>> X_new.shape
(569, 20)

See also

f_classif: ANOVA F-value between label/feature for classification tasks. mutual_info_classif: Mutual information for a discrete target. chi2: Chi-squared stats of non-negative features for classification tasks. f_regression: F-value between label/feature for regression tasks. mutual_info_regression: Mutual information for a continuous target. SelectPercentile: Select features based on percentile of the highest scores. SelectKBest: Select features based on the k highest scores. SelectFpr: Select features based on a false positive rate test. SelectFdr: Select features based on an estimated false discovery rate. SelectFwe: Select features based on family-wise error rate.

Full API documentation: GenericUnivariateSelectScikitsLearnNode

class mdp.nodes.BernoulliNBScikitsLearnNode

Naive Bayes classifier for multivariate Bernoulli models. This node has been automatically generated by wrapping the sklearn.naive_bayes.BernoulliNB class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Like MultinomialNB, this classifier is suitable for discrete data. The difference is that while MultinomialNB works with occurrence counts, BernoulliNB is designed for binary/boolean features.

Read more in the User Guide.

Parameters

alpha : float, optional (default=1.0)
Additive (Laplace/Lidstone) smoothing parameter (0 for no smoothing).
binarize : float or None, optional (default=0.0)
Threshold for binarizing (mapping to booleans) of sample features. If None, input is presumed to already consist of binary vectors.
fit_prior : boolean, optional (default=True)
Whether to learn class prior probabilities or not. If false, a uniform prior will be used.
class_prior : array-like, size=[n_classes,], optional (default=None)
Prior probabilities of the classes. If specified the priors are not adjusted according to the data.

Attributes

class_log_prior_ : array, shape = [n_classes]
Log probability of each class (smoothed).
feature_log_prob_ : array, shape = [n_classes, n_features]
Empirical log probability of features given a class, P(x_i|y).
class_count_ : array, shape = [n_classes]
Number of samples encountered for each class during fitting. This value is weighted by the sample weight when provided.
feature_count_ : array, shape = [n_classes, n_features]
Number of samples encountered for each (class, feature) during fitting. This value is weighted by the sample weight when provided.

Examples

>>> import numpy as np
>>> X = np.random.randint(2, size=(6, 100))
>>> Y = np.array([1, 2, 3, 4, 4, 5])
>>> from sklearn.naive_bayes import BernoulliNB
>>> clf = BernoulliNB()
>>> clf.fit(X, Y)
BernoulliNB(alpha=1.0, binarize=0.0, class_prior=None, fit_prior=True)
>>> print(clf.predict(X[2:3]))
[3]

References

C.D. Manning, P. Raghavan and H. Schuetze (2008). Introduction to Information Retrieval. Cambridge University Press, pp. 234-265.