Learning From Pairwise Confidence Comparisons and Unlabeled Data

Pairwise comparison classification is a recently thriving weakly-supervised model that generates a binary classifier based on feedback information from comparisons between unlabeled data pairs. However, limited by time and manpower, there are huge numbers of unlabeled samples in reality. These unlabeled samples not only provide valuable additional information at a relatively low cost but also contribute to improving the generalization ability of predictors. Pairwise comparison classification ignores unlabeled data points, resulting in a wastage of valuable data resources. To overcome this problem, this paper for the first time focuses on the case where the training set contains only pairwise confidence comparisons samples (PC) (one is more likely to be positive than the other) and unlabeled data points (U) (no label information), which is a new form of weakly-supervised learning method. We derive an unbiased risk estimator with theoretical guarantees and then present a risk correction to address possible overfitting. We also theoretically establish the estimation error bound and prove that the estimation error achieves the optimal parameter rate. Finally, experiments are conducted to validate the effectiveness of the proposed method.