Learning from not-all-negative pairwise data and unlabeled data

Abstract

A weakly-supervised approach utilizing data pairs with comparative or similarity/dissimilarity information has gained popularity in various fields due to its cost-effectiveness. However, the challenge of dealing with not all negative (i.e., pairwise data that includes at least one positive) or not all positive (i.e., pairwise data that includes at least one negative) data pairs has not been specifically addressed by any algorithm. To overcome this bottleneck, this paper explores a novelty weakly-supervision framework of learning from pairwise data that includes at least one positive and unlabeled data points ($P_{pos}U$) as a representative. The provided pairwise data ensures that each data pair contains at least one positive data point. Unlabeled data refers to data without labeled information. Firstly, this paper shows an unbiased risk estimator for $P_{pos}U$ data and use risk correction functions to mitigate the overfitting caused by negative terms. In addition, the estimation error bound is established for the empirical risk minimizer and the optimal convergence rate is obtained. Finally, the detailed experimental process and results are presented to demonstrate the effectiveness of the proposed method.