Neural Discriminant Analysis

Abstract

Statistical Discriminant Analysis is a classical technique in pattern matching with applications for classification problems and more general decision tasks. In this paper, we use a specific class of discriminant functions which we call product discriminant functions, or simply PDF's. Our main results for PDF's are the following: They are quite expressive, e.g., probability distributions defined by Chow-Expansions, Unique Probabilistic Automata or Unique Markov Models can also succinctly be written as PDF's. It is possible to obtain with high confidence almost optimal decisions for classification problems which can be modelled by PDF's. The number of training examples needed for that is bounded by a polynomial of low degree (in the relevant parameters). The evaluation of the training examples can be implemented on shallow neural nets.