Semi-analytical method for analyzing models and model selection measures based on moment analysis

Abstract

In this article we propose a moment-based method for studying models and model selection measures. By focusing on the probabilistic space of classifiers induced by the classification algorithm rather than on that of datasets, we obtain efficient characterizations for computing the moments, which is followed by visualization of the resulting formulae that are too complicated for direct interpretation. By assuming the data to be drawn independently and identically distributed from the underlying probability distribution, and by going over the space of all possible datasets, we establish general relationships between the generalization error, hold-out-set error, cross-validation error, and leave-one-out error. We later exemplify the method and the results by studying the behavior of the errors for the naive Bayes classifier.