Pointwise Binary Classification with Pairwise Confidence Comparisons

Ordinary (pointwise) binary classification aims to learn a binary classifier from pointwise labeled data. However, such pointwise labels may not be directly accessible due to privacy, confidentiality, or security considerations. In this case, can we still learn an accurate binary classifier? This paper proposes a novel setting, namely pairwise comparison (Pcomp) classification, where we are given only pairs of unlabeled data that we know one is more likely to be positive than the other, instead of pointwise labeled data. Pcomp classification is useful for private or subjective classification tasks. To solve this problem, we present a mathematical formulation for the generation process of pairwise comparison data, based on which we exploit an unbiased risk estimator(URE) to train a binary classifier by empirical risk minimization and establish an estimation error bound. We first prove that a URE can be derived and improve it using correction functions. Then, we start from the noisy-label learning perspective to introduce a progressive URE and improve it by imposing consistency regularization. Finally, experiments validate the effectiveness of our proposed solutions for Pcomp classification.