# Pointwise Binary Classification with Pairwise Confidence Comparisons

arXiv: https://arxiv.org/abs/2010.01875 · HTML: https://mlsanity.com/paper/2010.01875/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Oct 2020.

## Built on by (most cited first, 20 of 20)

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- [FastBUS: A Fast Bayesian Framework for Unified Weakly-Supervised Learning](https://mlsanity.com/paper/2603.00517/) (2026)
- [Binary Classification from Coupled Pairwise Labels](https://mlsanity.com/paper/2603.19713/) (2026)
- [Recent advances in weakly supervised learning: New supervision paradigms, assumption relaxations, and practical solutions](https://mlsanity.com/paper/2608.06896/) (2026)
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## Abstract (arXiv)

To alleviate the data requirement for training effective binary classifiers in binary classification, many weakly supervised learning settings have been proposed. Among them, some consider using pairwise but not pointwise labels, when pointwise labels are not accessible due to privacy, confidentiality, or security reasons. However, as a pairwise label denotes whether or not two data points share a pointwise label, it cannot be easily collected if either point is equally likely to be positive or negative. Thus, in this paper, we propose a novel setting called pairwise comparison (Pcomp) classification, where we have only pairs of unlabeled data that we know one is more likely to be positive than the other. Firstly, we give a Pcomp data generation process, derive an unbiased risk estimator (URE) with theoretical guarantee, and further improve URE using correction functions. Secondly, we link Pcomp classification to noisy-label learning to develop a progressive URE and improve it by imposing consistency regularization. Finally, we demonstrate by experiments the effectiveness of our methods, which suggests Pcomp is a valuable and practically useful type of pairwise supervision besides the pairwise label.