Tight Risk Bounds for Multi-Class Margin Classifiers

TL;DR

This paper introduces a new, tight risk bound for large-margin multi-class classifiers that accounts for the classifier's marginal distribution and hypothesis complexity, improving understanding of classifier performance.

Contribution

It presents a novel risk bound for multi-class classifiers that is tight in the number of classes and includes a simplified version for kernel-based hypotheses.

Findings

The proposed bound is tight in the number of classes.

Comparison shows the bound is sharper than previous bounds.

A simplified bound is provided for kernel-based hypotheses.

Abstract

We consider a problem of risk estimation for large-margin multi-class classifiers. We propose a novel risk bound for the multi-class classification problem. The bound involves the marginal distribution of the classifier and the Rademacher complexity of the hypothesis class. We prove that our bound is tight in the number of classes. Finally, we compare our bound with the related ones and provide a simplified version of the bound for the multi-class classification with kernel based hypotheses.