Sparse Reject Option Classifier Using Successive Linear Programming

Abstract

In this paper, we propose an approach for learning sparse reject option classifiers using double ramp loss L_dr. We use DC programming to find the risk minimizer. The algorithm solves a sequence of linear programs to learn the reject option classifier. We show that the loss L_dr is Fisher consistent. We also show that the excess risk of loss L_d is upper bounded by excess risk of L_dr. We derive the generalization error bounds for the proposed approach. We show the effectiveness of the proposed approach by experimenting it on several real world datasets. The proposed approach not only performs comparable to the state of the art, it also successfully learns sparse classifiers.