# PUe: Biased Positive-Unlabeled Learning Enhancement by Causal Inference

arXiv: https://arxiv.org/abs/2607.13428 · HTML: https://mlsanity.com/paper/2607.13428/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 24 references that are in the map.
- First posted on arXiv 15 Jul 2026.

## Builds on (most cited first, 6 of 6)

- [Positive-Unlabeled Learning with Non-Negative Risk Estimator](https://mlsanity.com/paper/1703.00593/) (2017)
- [Learning from positive and unlabeled data: a survey](https://mlsanity.com/paper/1811.04820/) (2018)
- [Self-PU: Self Boosted and Calibrated Positive-Unlabeled Training](https://mlsanity.com/paper/2006.11280/) (2020)
- [Dist-PU: Positive-Unlabeled Learning from a Label Distribution Perspective](https://mlsanity.com/paper/2212.02801/) (2022)
- [Beyond the Selected Completely At Random Assumption for Learning from Positive and Unlabeled Data](https://mlsanity.com/paper/1809.03207/) (2018)
- [Classification from Positive, Unlabeled and Biased Negative Data](https://mlsanity.com/paper/1810.00846/) (2018)

## Abstract (arXiv)

Positive-Unlabeled (PU) learning aims to achieve high-accuracy binary classification with limited labeled positive examples and numerous unlabeled ones. Existing cost-sensitive-based methods often rely on strong assumptions that examples with an observed positive label were selected entirely at random. In fact, the uneven distribution of labels is prevalent in real-world PU problems, indicating that most actual positive and unlabeled data are subject to selection bias. Building on the SAR-PU propensity-weighted framework of Bekker et al., we study a PU learning enhancement (PUe) framework using normalized propensity scores and normalized inverse probability weighting (NIPW). PUe's main contributions are a normalized inverse-probability-weighted PU risk formulation; additional theoretical analyses of normalized sample-weight error and common PU estimators under biased labeling; regularized deep propensity-score estimation; integration with modern cost-sensitive PU methods; and support for selectively labeled negative classes. Experiments on MNIST, CIFAR-10, and ADNI demonstrate improvements over several PU baselines under non-uniform label distributions.