Lasso type classifiers with a reject option

TL;DR

This paper introduces a method for binary classification that allows the classifier to abstain from making a decision at a certain cost, using a lasso-type penalty to control the excess risk.

Contribution

It provides a simple proof of the oracle inequality for excess risk in classifiers with a reject option employing a lasso penalty.

Findings

Established an oracle inequality for the excess risk

Demonstrated the effectiveness of the reject option in classification

Provided theoretical guarantees for lasso-based classifiers

Abstract

We consider the problem of binary classification where one can, for a particular cost, choose not to classify an observation. We present a simple proof for the oracle inequality for the excess risk of structural risk minimizers using a lasso type penalty.