Title: On Symmetric Losses for Learning from Corrupted Labels,
Abstract: This paper aims to provide a better understanding of a symmetric loss. First,
we show 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 on BER and AUC optimization from corrupted labels to
validate the relevance of the symmetric condition.