Model Browser User's Guide

GCV Criterion

Generalized cross-validation(GCV) is a measure of the goodness of fit of a model to the data that is minimized when the residuals are small, but not so small that the network has overfitted the data. It is easy to compute, and networks with small GCV values should have good predictive capability. It is related to the PRESS statistic.

The definition of GCV is given by Orr (4, see References).

where y is the target vector, and P is the projection matrix, given by I - XA^-1X^T. An important feature of using GCV as a criterion for determining the optimal network in our fit algorithms is the existence of update formulas for the regularization parameter . These update formulas are obtained by differentiating GCV with respect to and setting the result to zero. That is, they are based on gradient-descent.

This gives the general equation (from Orr, 6, References)

We now specialize these formulas to the case of ridge regression and to the Rols algorithm.

Statistics

GCV for Ridge Regression