Probabilistic Vector Machines

Abstract

This paper proposes a novel Support Vector Machine (SVM) methodology for finding accurate probabilities of class memberships in supervised classification problems. Classical SVMs do not complement their class predictions with reliable confidence measures for each class assignment. For two-class problems this problem can be overcome by combining a sequence of weighted SVMs predictions into consistent class probabilities. In this work we show how a smart use of mathematical programming models can be used to extend this approach to the general multi-class classification problem. Previous attempts to tackle this problem either do not scale well with the number of different classes, or rely on sub-optimal partition strategies. Numerical experiments reveal the good scaling properties of the proposal, and the relative advantages of its class probability estimates over alternative approaches.