Multiclass learning with margin: exponential rates with no bias-variance trade-off

TL;DR

This paper demonstrates that under certain margin conditions, multiclass classifiers can achieve exponential error decay without bias-variance trade-offs, generalizing binary results to multiclass scenarios.

Contribution

It extends known binary margin error bounds to multiclass classification, showing exponential convergence rates without bias-variance trade-offs under various margin assumptions.

Findings

Error bounds decrease exponentially under margin conditions

Different margin assumptions yield different convergence rates

Results generalize binary margin bounds to multiclass setting

Abstract

We study the behavior of error bounds for multiclass classification under suitable margin conditions. For a wide variety of methods we prove that the classification error under a hard-margin condition decreases exponentially fast without any bias-variance trade-off. Different convergence rates can be obtained in correspondence of different margin assumptions. With a self-contained and instructive analysis we are able to generalize known results from the binary to the multiclass setting.