Max-Min Posterior Pseudo-Probabilities Estimation of Posterior Class Probabilities to Maximize Class Separability

The estimation of the posterior class probabilities is desirable for optimal decision, decision confidence measure, and accurate performance evaluation of a classifier. In this paper, we address the problem of estimating posterior class probabilities by learning from samples for producing optimal classifiers. We introduce a posterior pseudo-probability function based on Bayes’ formula to transform class-conditional probability values into posterior class probability values. The parameters in this function are trained from the data using the proposed max-min posterior pseudo-probability method in which the optimization objective is to maximize the posterior pseudo-probabilities for positive samples, at the same time to minimize those for negative samples. We show the effectiveness of our estimator in learning pattern classification through the experimental results in three applications: content-based image retrieval, text extraction, and handwritten digit recognition.