Objective Functions For Neural Network Classifier Design

Abstract

Backpropagation was originally derived in the context of minimizing a mean-squared error (MSE) objective function. More recently there has been interest in objective functions that provide accurate class probability estimates. In this talk we derive necessary and sufficient conditions on the required form of an objective function to provide probability estimates. This leads to the definition of a general class of functions which includes MSE and cross entropy (CE) as two of the simplest cases. We establish the equivalence of these functions to Maximum Likelihood estimation and the more general principle of Minimum Description Length models. Empirical results are used to demonstrate the tradeoffs associated with the choice of objective functions which minimize to a probability.