On Symmetric Losses for Learning from Corrupted Labels

TL;DR

This paper investigates symmetric loss functions for learning with corrupted labels, providing theoretical insights, proposing a convex barrier hinge loss, and validating the benefits through experiments.

Contribution

It offers a comprehensive theoretical analysis of symmetric losses, introduces a new convex barrier hinge loss, and empirically demonstrates their advantages in corrupted label scenarios.

Findings

Symmetric losses are beneficial for BER and AUC maximization with corrupted labels.

Theoretical properties such as calibration and consistency are established for symmetric losses.

The proposed convex barrier hinge loss improves learning performance under label corruption.

Abstract

This paper aims to provide a better understanding of a symmetric loss. First, we emphasize that using a symmetric loss is advantageous in the balanced error rate (BER) minimization and area under the receiver operating characteristic curve (AUC) maximization from corrupted labels. Second, we prove general theoretical properties of symmetric losses, including a classification-calibration condition, excess risk bound, conditional risk minimizer, and AUC-consistency condition. Third, since all nonnegative symmetric losses are non-convex, we propose a convex barrier hinge loss that benefits significantly from the symmetric condition, although it is not symmetric everywhere. Finally, we conduct experiments to validate the relevance of the symmetric condition.