On Symmetric Losses for Learning from Corrupted Labels

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Nontawat Charoenphakdee, Jongyeong Lee, Masashi Sugiyama ;
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:961-970, 2019.

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.

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