# Learning from Positive and Unlabeled Data under the Selected At Random Assumption

arXiv: https://arxiv.org/abs/1808.08755 · HTML: https://mlsanity.com/paper/1808.08755/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Aug 2018.

## Built on by (most cited first, 5 of 5)

- [Automatic Debiased Learning from Positive, Unlabeled, and Exposure Data](https://mlsanity.com/paper/2303.04797/) (2023)
- [On the Necessity of World Knowledge for Mitigating Missing Labels in Extreme Classification](https://mlsanity.com/paper/2408.09585/) (2024)
- [Learning from Double Positive and Unlabeled Data for Potential-Customer Identification](https://mlsanity.com/paper/2506.00436/) (2025)
- [Positive-Unlabeled Preference Optimization For Chest X-ray Report Generation](https://mlsanity.com/paper/2608.05341/) (2026)
- [Positive-Unlabeled Learning for Agent Safety False Alarm Auditing](https://mlsanity.com/paper/2610.02925/) (2026)

## Abstract (arXiv)

For many interesting tasks, such as medical diagnosis and web page classification, a learner only has access to some positively labeled examples and many unlabeled examples. Learning from this type of data requires making assumptions about the true distribution of the classes and/or the mechanism that was used to select the positive examples to be labeled. The commonly made assumptions, separability of the classes and positive examples being selected completely at random, are very strong. This paper proposes a weaker assumption that assumes the positive examples to be selected at random, conditioned on some of the attributes. To learn under this assumption, an EM method is proposed. Experiments show that our method is not only very capable of learning under this assumption, but it also outperforms the state of the art for learning under the selected completely at random assumption.