Class GaussianProcessScikitsLearnNode

The Gaussian Process model class. This node has been automatically generated by wrapping the scikits.learn.gaussian_process.gaussian_process.GaussianProcess class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Parameters

regr : string or callable, optional

A regression function returning an array of outputs of the linear regression functional basis. The number of observations n_samples should be greater than the size p of this basis. Default assumes a simple constant regression trend. Here is the list of built-in regression models:

• 'constant', 'linear', 'quadratic'

corr : string or callable, optional

A stationary autocorrelation function returning the autocorrelation between two points x and x'. Default assumes a squared-exponential autocorrelation model. Here is the list of built-in correlation models:

• 'absolute_exponential', 'squared_exponential',
• 'generalized_exponential', 'cubic', 'linear'

beta0 : double array_like, optional

The regression weight vector to perform Ordinary Kriging (OK). Default assumes Universal Kriging (UK) so that the vector beta of regression weights is estimated using the maximum likelihood principle.

storage_mode : string, optional

A string specifying whether the Cholesky decomposition of the correlation matrix should be stored in the class (storage_mode = 'full') or not (storage_mode = 'light'). Default assumes storage_mode = 'full', so that the Cholesky decomposition of the correlation matrix is stored. This might be a useful parameter when one is not interested in the MSE and only plan to estimate the BLUP, for which the correlation matrix is not required.

verbose : boolean, optional

A boolean specifying the verbose level. Default is verbose = False.

theta0 : double array_like, optional

An array with shape (n_features, ) or (1, ). The parameters in the autocorrelation model. If thetaL and thetaU are also specified, theta0 is considered as the starting point for the maximum likelihood rstimation of the best set of parameters. Default assumes isotropic autocorrelation model with theta0 = 1e-1.

thetaL : double array_like, optional

An array with shape matching theta0's. Lower bound on the autocorrelation parameters for maximum likelihood estimation. Default is None, so that it skips maximum likelihood estimation and it uses theta0.

thetaU : double array_like, optional

An array with shape matching theta0's. Upper bound on the autocorrelation parameters for maximum likelihood estimation. Default is None, so that it skips maximum likelihood estimation and it uses theta0.

normalize : boolean, optional

Input X and observations y are centered and reduced wrt means and standard deviations estimated from the n_samples observations provided. Default is normalize = True so that data is normalized to ease maximum likelihood estimation.

nugget : double, optional

Introduce a nugget effect to allow smooth predictions from noisy data. Default assumes a nugget close to machine precision for the sake of robustness (nugget = 10. * MACHINE_EPSILON).

optimizer : string, optional

A string specifying the optimization algorithm to be used. Default uses 'fmin_cobyla' algorithm from scipy.optimize. Here is the list of available optimizers:

• 'fmin_cobyla', 'Welch'

'Welch' optimizer is dued to Welch et al., see reference [2]. It consists in iterating over several one-dimensional optimizations instead of running one single multi-dimensional optimization.

random_start : int, optional

The number of times the Maximum Likelihood Estimation should be performed from a random starting point. The first MLE always uses the specified starting point (theta0), the next starting points are picked at random according to an exponential distribution (log-uniform on [thetaL, thetaU]). Default does not use random starting point (random_start = 1).

Example

>>> import numpy as np
>>> from scikits.learn.gaussian_process import GaussianProcess
>>> X = np.atleast_2d([1., 3., 5., 6., 7., 8.]).T
>>> y = (X * np.sin(X)).ravel()
>>> gp = GaussianProcess(theta0=0.1, thetaL=.001, thetaU=1.)
>>> gp.fit(X, y) # doctest: +ELLIPSIS
GaussianProcess(normalize=True, ...)

Implementation details

The presentation implementation is based on a translation of the DACE Matlab toolbox, see reference [1].

References

[1] H.B. Nielsen, S.N. Lophaven, H. B. Nielsen and J. Sondergaard (2002).

DACE - A MATLAB Kriging Toolbox. http://www2.imm.dtu.dk/~hbn/dace/dace.pdf

[2] W.J. Welch, R.J. Buck, J. Sacks, H.P. Wynn, T.J. Mitchell, and M.D.

Morris (1992). Screening, predicting, and computer experiments. Technometrics, 34(1) 15--25. http://www.jstor.org/pss/1269548

Overrides: object.__init__

This function evaluates the Gaussian Process model at x. This node has been automatically generated by wrapping the scikits.learn.gaussian_process.gaussian_process.GaussianProcess class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Parameters

X : array_like

An array with shape (n_eval, n_features) giving the point(s) at which the prediction(s) should be made.

eval_MSE : boolean, optional

A boolean specifying whether the Mean Squared Error should be evaluated or not. Default assumes evalMSE = False and evaluates only the BLUP (mean prediction).

batch_size : integer, optional

An integer giving the maximum number of points that can be evaluated simulatneously (depending on the available memory). Default is None so that all given points are evaluated at the same time.

Returns

y : array_like

An array with shape (n_eval, ) with the Best Linear Unbiased Prediction at x.

MSE : array_like, optional (if eval_MSE == True)

An array with shape (n_eval, ) with the Mean Squared Error at x.

Overrides: Node.execute

Overrides: Node.is_invertible

(inherited documentation)

Returns: bool

A boolean indicating whether the node can be trained.

Overrides: Node.is_trainable

The Gaussian Process model fitting method. This node has been automatically generated by wrapping the scikits.learn.gaussian_process.gaussian_process.GaussianProcess class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Parameters

X : double array_like

An array with shape (n_samples, n_features) with the input at which observations were made.

y : double array_like

An array with shape (n_features, ) with the observations of the scalar output to be predicted.

Returns

gp : self

A fitted Gaussian Process model object awaiting data to perform predictions.

Overrides: Node.stop_training