6.5 Regularization parameter selection

We have to this point avoided the question of how to choose the parameter c06-math-299 that appears in the penalized least-squares criterion. There are several data adaptive techniques that are typically used for this purpose. We will describe three of them that are appropriate for the scenario that was examinedin the previous section: namely, where c06-math-300 and c06-math-301 for c06-math-302 finite dimensional with basis c06-math-303. As before the squared norm for c06-math-304 is taken to be

equation

We begin with ordinary cross validation. Let c06-math-305 be the minimizer of

equation

and define

Ordinary cross validation then picks to minimize ...

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