Pareto optimal linear classification

We consider the problem of choosing a lin- ear classier that minimizes misclassication probabilities in two-class classication, which is a bi-criterion problem, involving a trade-o between two objectives. We assume that the class-conditional distributions are Gaussian. This assumption makes it computationally tractable to nd Pareto optimal linear clas- siers whose classication capabilities are in- ferior to no other linear ones. The main pur- pose of this paper is to establish several ro- bustness properties of those classiers with respect to variations and uncertainties in the distributions. We also extend the results to kernel-based classication. Finally, we show how to carry out trade-o analysis empiri- cally with a nite number of given labeled data.