# 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.