  Weakly supervised learning aims to empower machine learning when the perfect
supervision is unavailable, which has drawn great attention from researchers.
Among various types of weak supervision, one of the most challenging cases is
to learn from multiple unlabeled (U) datasets with only a little knowledge of
the class priors, or U$^m$ learning for short. In this paper, we study the
problem of building an AUC (area under ROC curve) optimization model from
multiple unlabeled datasets, which maximizes the pairwise ranking ability of
the classifier. We propose U$^m$-AUC, an AUC optimization approach that
converts the U$^m$ data into a multi-label AUC optimization problem, and can be
trained efficiently. We show that the proposed U$^m$-AUC is effective
theoretically and empirically.
