Sparse and Robust Reject Option Classifier using Successive Linear Programming

In this paper, we propose a new sparse and robust reject option classifier based on minimization of $l_1$ regularized risk under double ramp loss $L_{dr,\rho}$. We use DC programming to find the risk minimizer. The algorithm solves a sequence of linear programs to learn the reject option classifier. Moreover, we show that the risk under $L_{dr,\rho}$ is minimized by generalized Bayes classifier in the reject option setting. We also provide the excess risk bound for $L_{dr,\rho}$. We show the effectiveness of the proposed approach by experimenting it on several real world datasets.