Cross-Validation Estimates IMSE

Let zN denote a given set of N training examples. Let QN(zN) denote the expected squared error (the expectation taken over all possible examples) of the network after being trained on zN. This measures the quality of fit afforded by training on a given set of N examples. Let IMSEN denote the Integrated Mean Squared Error for training sets of size N. Given reasonable assumptions, it is straightforward to show that IMSEN E[Q N(ZN)] - 0"2, where the expectation is now over all training sets of size N, ZN is a random training set of size N, and 0"2 is the noise variance. Let CN CN(zN) denote the "delete-one cross-validation" squared error measure for a network trained on zN.