Robust Classifiers Using Imprecise Probability Models and Importance of Classes

Abstract

A framework for constructing robust classification models is proposed in the paper. An assumption about importance of one of the classes in comparison with other classes is incorporated into the models. It often takes place in the real application, for example, in reliability, in medical diagnostic, etc. A main idea underlying the models is to consider a set of probability distributions on training examples produced by the imprecise probability models such as linear-vacuous mixture and constant odd-ratio contaminated models. Extreme points of the sets of probability distributions are a main tool for constructing the robust classifiers. It is shown that algorithms for computing optimal classification parameters are reduced to a finite number of weighted support vector machines with weights determined by the extreme points. Experimental results with synthetic and real data illustrate the proposed models.