6.7.5.2.1. statsmodels.sandbox.regression.kernridgeregress_class.GaussProcess¶

class statsmodels.sandbox.regression.kernridgeregress_class.GaussProcess(x, y=None, kernel=<function kernel_rbf>, scale=0.5, ridgecoeff=1e-10, **kwds)[source]¶

class to perform kernel ridge regression (gaussian process)

Warning: this class is memory intensive, it creates nobs x nobs distance matrix and its inverse, where nobs is the number of rows (observations). See sparse version for larger number of observations

Notes

Todo: * normalize multidimensional x array on demand, either by var or cov * add confidence band * automatic selection or proposal of smoothing parameters

Note: this is different from kernel smoothing regression,

see for example http://en.wikipedia.org/wiki/Kernel_smoother

In this version of the kernel ridge regression, the training points are fitted exactly. Needs a fast version for leave-one-out regression, for fitting each observation on all the other points. This version could be numerically improved for the calculation for many different values of the ridge coefficient. see also short summary by Isabelle Guyon (ETHZ) in a manuscript KernelRidge.pdf

Needs verification and possibly additional statistical results or summary statistics for interpretation, but this is a problem with non-parametric, non-linear methods.

Parameters:

x : 2d array (N,K) data array of explanatory variables, columns represent variables rows represent observations y : 2d array (N,1) (optional) endogenous variable that should be fitted or predicted can alternatively be specified as parameter to fit method kernel : function, default: kernel_rbf kernel: (x1,x2)->kernel matrix is a function that takes as parameter two column arrays and return the kernel or distance matrix scale : float (optional) smoothing parameter for the rbf kernel ridgecoeff : float (optional) coefficient that is multiplied with the identity matrix in the ridge regression

Notes

After initialization, kernel matrix is calculated and if y is given as parameter then also the linear regression parameter and the fitted or estimated y values, yest, are calculated. yest is available as an attribute in this case.

Both scale and the ridge coefficient smooth the fitted curve.

__init__(x, y=None, kernel=<function kernel_rbf>, scale=0.5, ridgecoeff=1e-10, **kwds)[source]¶

Parameters:

x : 2d array (N,K) data array of explanatory variables, columns represent variables rows represent observations y : 2d array (N,1) (optional) endogenous variable that should be fitted or predicted can alternatively be specified as parameter to fit method kernel : function, default: kernel_rbf kernel: (x1,x2)->kernel matrix is a function that takes as parameter two column arrays and return the kernel or distance matrix scale : float (optional) smoothing parameter for the rbf kernel ridgecoeff : float (optional) coefficient that is multiplied with the identity matrix in the ridge regression

Notes

After initialization, kernel matrix is calculated and if y is given as parameter then also the linear regression parameter and the fitted or estimated y values, yest, are calculated. yest is available as an attribute in this case.

Both scale and the ridge coefficient smooth the fitted curve.