On the algorithmic implementation of stochastic discrimination

Stochastic discrimination is a general methodology for constructing classifiers appropriate for pattern recognition. It is based on combining arbitrary numbers of very weak components, which are usually generated by some pseudorandom process, and it has the property that the very complex and accurate classifiers produced in this way retain the ability, characteristic of their weak component pieces, to generalize to new data. In fact, it is often observed, in practice, that classifier performance on test sets continues to rise as more weak components are added, even after performance on training sets seems to have reached a maximum. This is predicted by the underlying theory, for even though the formal error rate on the training set may have reached a minimum, more sophisticated measures intrinsic to this method indicate that classifier performance on both training and test sets continues to improve as complexity increases. We begin with a review of the method of stochastic discrimination as applied to pattern recognition. Through a progression of examples keyed to various theoretical issues, we discuss considerations involved with its algorithmic implementation. We then take such an algorithmic implementation and compare its performance, on a large set of standardized pattern recognition problems from the University of California Irvine, and Statlog collections, to many other techniques reported on in the literature, including boosting and bagging. In doing these studies, we compare our results to those reported in the literature by the various authors for the other methods, using the same data and study paradigms used by them. Included in the paper is an outline of the underlying mathematical theory of stochastic discrimination and a remark concerning boosting, which provides a theoretical justification for properties of that method observed in practice, including its ability to generalize.