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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 PDF's simply. Our main results for PDF's are the following:

  • They are very 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. The net parameters are adjusted by a variant of the Hebbian learning rule.