  When minimizing the empirical risk in binary classification, it is a common
practice to replace the zero-one loss with a surrogate loss to make the
learning objective feasible to optimize. Examples of well-known surrogate
losses for binary classification include the logistic loss, hinge loss, and
sigmoid loss. It is known that the choice of a surrogate loss can highly
influence the performance of the trained classifier and therefore it should be
carefully chosen. Recently, surrogate losses that satisfy a certain symmetric
condition (aka., symmetric losses) have demonstrated their usefulness in
learning from corrupted labels. In this article, we provide an overview of
symmetric losses and their applications. First, we review how a symmetric loss
can yield robust classification from corrupted labels in balanced error rate
(BER) minimization and area under the receiver operating characteristic curve
(AUC) maximization. Then, we demonstrate how the robust AUC maximization method
can benefit natural language processing in the problem where we want to learn
only from relevant keywords and unlabeled documents. Finally, we conclude this
article by discussing future directions, including potential applications of
symmetric losses for reliable machine learning and the design of non-symmetric
losses that can benefit from the symmetric condition.
