  Since acquiring perfect supervision is usually difficult, real-world machine
learning tasks often confront inaccurate, incomplete, or inexact supervision,
collectively referred to as weak supervision. In this work, we present WSAUC, a
unified framework for weakly supervised AUC optimization problems, which covers
noisy label learning, positive-unlabeled learning, multi-instance learning, and
semi-supervised learning scenarios. Within the WSAUC framework, we first frame
the AUC optimization problems in various weakly supervised scenarios as a
common formulation of minimizing the AUC risk on contaminated sets, and
demonstrate that the empirical risk minimization problems are consistent with
the true AUC. Then, we introduce a new type of partial AUC, specifically, the
reversed partial AUC (rpAUC), which serves as a robust training objective for
AUC maximization in the presence of contaminated labels. WSAUC offers a
universal solution for AUC optimization in various weakly supervised scenarios
by maximizing the empirical rpAUC. Theoretical and experimental results under
multiple settings support the effectiveness of WSAUC on a range of weakly
supervised AUC optimization tasks.
