  Weakly supervised learning has drawn considerable attention recently to
reduce the expensive time and labor consumption of labeling massive data. In
this paper, we investigate a novel weakly supervised learning problem of
learning from similarity-confidence (Sconf) data, where we aim to learn an
effective binary classifier from only unlabeled data pairs equipped with
confidence that illustrates their degree of similarity (two examples are
similar if they belong to the same class). To solve this problem, we propose an
unbiased estimator of the classification risk that can be calculated from only
Sconf data and show that the estimation error bound achieves the optimal
convergence rate. To alleviate potential overfitting when flexible models are
used, we further employ a risk correction scheme on the proposed risk
estimator. Experimental results demonstrate the effectiveness of the proposed
methods.
