Neural Discriminant Models, Bootstrapping, and Simulation

Abstract

This paper considers the feed-forward neural network models for data of mutually exclusive groups and a set of predictor variables. We take into account the bootstrapping based on information criterion when selecting the optimum number of hidden units for a neural network model and the deviance in order to summarize the measure of goodness-of-fit on fitted neural network models. The bootstrapping is also adapted in order to provide estimates of the bias of the excess error in a prediction rule constructed with training samples. Simulated data from known (true) models are analyzed in order to interpret the results using the neural network. In addition, the thyroid disease database, which compares estimated measures of predictive performance, is examined in both a pure training sample study and in a test sample study, in which the realized test sample apparent error rates associated with a constructed prediction rule are reported. Apartment house data of the metropolitan area station with four-class classification are also analyzed in order to assess the bootstrapping by comparing leaving-one-out cross-validation (CV).