Cross-Validation Estimates IMSE

Abstract

Integrated Mean Squared Error (IMSE) is a version of the usual mean squared error criterion, averaged over all possible training sets of a given size. If it could be observed, it could be used to determine optimal network complexity or optimal data subsets for efficient training. We show that two common methods of cross-validating average squared error deliver unbiased estimates of IMSE, converging to IMSE with probability one. These estimates thus make possible approximate IMSE-based choice of network complexity. We also show that two variants of cross validation measure provide unbiased IMSE-based estimates potentially useful for selecting optimal data subsets.