Hampshire, John B. and Pearlmutter, Barak A. (1990) Equivalence Proofs for Multi-Layer Perceptron Classifiers and the Bayesian Discriminant Function. Proceedings of the 1990 Connectionist Models Summer School. ISSN 0-55860-156-2

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Abstract

This paper presents a number of proofs that equate the outputs of a Multi-Layer Perceptron (MLP) classifier and the optimal Bayesian discriminant function for asymptotically large sets of statistically independent training samples. Two broad classes of objective functions are shown to yield Bayesian discriminant performance. The first class are “reasonable error measures,” which achieve Bayesian discriminant performance by engendering classifier outputs that asymptotically equate to a posteriori probabilities. This class includes the mean-squared error (MSE) objective function as well as a number of information theoretic objective functions. The second class are classification figures of merit (CFMmono ), which yield a qualified approximation to Bayesian discriminant performance by engendering classifier outputs that asymptotically identify themaximum a posteriori probability for a given input. Conditions and relationships for Bayesian discriminant functional equivalence are given for both classes of objective functions. Differences between the two classes are then discussed very briefly in the context of how they might affect MLP classifier generalization, given relatively small training sets.

Item Type:	Article
Keywords:	Multi-Layer Perceptron Classifiers; Bayesian Discriminant Function;
Academic Unit:	Faculty of Science and Engineering > Computer Science Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID:	5504
Depositing User:	Barak Pearlmutter
Date Deposited:	15 Oct 2014 13:22
Journal or Publication Title:	Proceedings of the 1990 Connectionist Models Summer School
Publisher:	Morgan Kaufmann Publishers
Refereed:	Yes
URI:
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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