Robust AUC maximization for classification with pairwise confidence comparisons

Supervised learning often requires a large number of labeled examples, which has become a critical bottleneck in the case that manual annotating the class labels is costly. To mitigate this issue, a new framework called pairwise comparison (Pcomp) classification is proposed to allow training examples only weakly annotated with pairwise comparison, i.e., which one of two examples is more likely to be positive. The previous study solves Pcomp problems by minimizing the classification error, which may lead to less robust model due to its sensitivity to class distribution. In this paper, we propose a robust learning framework for Pcomp data along with a pairwise surrogate loss called Pcomp-AUC. It provides an unbiased estimator to equivalently maximize AUC without accessing the precise class labels. Theoretically, we prove the consistency with respect to AUC and further provide the estimation error bound for the proposed method. Empirical studies on multiple datasets validate the effectiveness of the proposed method.