Sparse Reject Option Classifier Using Successive Linear Programming

TL;DR

This paper introduces a novel sparse reject option classifier using double ramp loss and successive linear programming, demonstrating theoretical consistency and practical effectiveness on real datasets.

Contribution

It presents a new method combining double ramp loss with DC programming for sparse reject classifiers, with proven Fisher consistency and generalization bounds.

Findings

Performs comparably to state-of-the-art methods

Successfully learns sparse classifiers

Validated on multiple real-world datasets

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 the 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 but it also successfully learns sparse classifiers.