GCV COST
Computes the cost associated to the Generalized Cross Validation technique for a given value of lambda.
Contents
Function of MOBY-DIC TOOLBOX.
Description
Consider the regularized least squares problem:
and H = G'G, Q = L'L;
The choice of parameter lambda is a very critical task. One way to choose it is to minimize the following cost function:
being n the number of elements of array d, the k-th element of array d and
the k-th element of array
, with
obtained by solving problem (1) considering all data d except for ith k-th element
. It is a sort of prediction error on the data which has not been considered in the optimization problem.
The cost function (2) can be expressed in a more computationally convenient way in this way:
being the element in k-th row and k-th column of matrix
, and
.
Syntax
V = GCVcost(H, Q, G, d, w, lambda)
Acknowledgements
Contributors:
- Alberto Oliveri (alberto.oliveri@unige.it)
Copyright is with:
- Copyright (C) 2012 University of Genoa, Italy.