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
