Ranking functions, perceptrons, and associated probabilities

Abstract

The paper is motivated by a ranking problem arising e.g. in financial institutions. This ranking problem is reduced to a system of inequalities that may be solved by applying the perceptron learning theorem. Under certain additional assumptions the associated probabilities are derived by exploiting Bayes' Theorem. It is shown that from these a posteriori probabilities the original classifier may be recovered. On the other hand, assuming that perfect classification is possible, a maximum likelihood solution is derived from the classifier. Some experimental results are given. © Springer-Verlag Berlin Heidelberg 2005.