Learning class probabilities from labeled data

A Bayesian classifier may supply an optimal estimate of the a posteriori class probabilities for classifying stochastic patterns, provided that the underlying statistical model of the problem is known. In the absence of such a priori knowledge, one valuable alternative is the Boltzmann perceptron classifier (BPC), a statistical neural based classifier, which was shown to have the capability of Bayesian like decisions. The original learning algorithm of the BPC requires a knowledge of the a posteriori probabilities for the given training set. However, these probabilities are seldom known in advance, and instead, labeled training data is given for which only the class membership associated with each training sample is known. The authors introduce a regulated learning scheme which estimates the class probabilities from such labeled data and constructs a classifier that generalizes well for new data