# Rethinking Class-Prior Estimation for Positive-Unlabeled Learning

arXiv: https://arxiv.org/abs/2002.03673 · HTML: https://mlsanity.com/paper/2002.03673/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Feb 2020.

## Built on by (most cited first, 15 of 15)

- [Sample Selection with Uncertainty of Losses for Learning with Noisy Labels](https://mlsanity.com/paper/2106.00445/) (2021)
- [Binary Classification with Confidence Difference](https://mlsanity.com/paper/2310.05632/) (2023)
- [Learning with Complementary Labels Revisited: The Selected-Completely-at-Random Setting Is More Practical](https://mlsanity.com/paper/2311.15502/) (2023)
- [Mixture Proportion Estimation Beyond Irreducibility](https://mlsanity.com/paper/2306.01253/) (2023)
- [Making Binary Classification from Multiple Unlabeled Datasets Almost Free of Supervision](https://mlsanity.com/paper/2306.07036/) (2023)
- [Rethinking Consistent Multi-Label Classification Under Inexact Supervision](https://mlsanity.com/paper/2510.04091/) (2025)
- [Unraveling the Impact of Heterophilic Structures on Graph Positive-Unlabeled Learning](https://mlsanity.com/paper/2405.19919/) (2024)
- [Meta-learning for Positive-unlabeled Classification](https://mlsanity.com/paper/2406.03680/) (2024)
- [Novel Node Category Detection Under Subpopulation Shift](https://mlsanity.com/paper/2404.01216/) (2024)
- [Accessible, Realistic, and Fair Evaluation of Positive-Unlabeled Learning Algorithms](https://mlsanity.com/paper/2509.24228/) (2025)
- [Classification from Positive and Biased Negative Data with Skewed Labeled Posterior Probability](https://mlsanity.com/paper/2203.05749/) (2022)
- [Learning from Ambiguous Data with Hard Labels](https://mlsanity.com/paper/2501.01844/) (2025)
- [Mixture Proportion Estimation and Weakly-supervised Kernel Test for Conditional Independence](https://mlsanity.com/paper/2604.07191/) (2026)
- [Recent advances in weakly supervised learning: New supervision paradigms, assumption relaxations, and practical solutions](https://mlsanity.com/paper/2608.06896/) (2026)
- [Partial AUC Maximization from Positive-unlabeled Data](https://mlsanity.com/paper/2610.00284/) (2026)

## Abstract (arXiv)

Given only positive (P) and unlabeled (U) data, PU learning can train a binary classifier without any negative data. It has two building blocks: PU class-prior estimation (CPE) and PU classification; the latter has been well studied while the former has received less attention. Hitherto, the distributional-assumption-free CPE methods rely on a critical assumption that the support of the positive data distribution cannot be contained in the support of the negative data distribution. If this is violated, those CPE methods will systematically overestimate the class prior; it is even worse that we cannot verify the assumption based on the data. In this paper, we rethink CPE for PU learning-can we remove the assumption to make CPE always valid? We show an affirmative answer by proposing Regrouping CPE (ReCPE) that builds an auxiliary probability distribution such that the support of the positive data distribution is never contained in the support of the negative data distribution. ReCPE can work with any CPE method by treating it as the base method. Theoretically, ReCPE does not affect its base if the assumption already holds for the original probability distribution; otherwise, it reduces the positive bias of its base. Empirically, ReCPE improves all state-of-the-art CPE methods on various datasets, implying that the assumption has indeed been violated here.