# Focused PU learning from imbalanced data

arXiv: https://arxiv.org/abs/2605.14467 · HTML: https://mlsanity.com/paper/2605.14467/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 67 references that are in the map.
- First posted on arXiv 14 May 2026.

## Builds on (most cited first, 13 of 13)

- [TabTransformer: Tabular Data Modeling Using Contextual Embeddings](https://mlsanity.com/paper/2012.06678/) (2020)
- [Pay Attention to MLPs](https://mlsanity.com/paper/2105.08050/) (2021)
- [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)
- [Mixture Proportion Estimation via Kernel Embedding of Distributions](https://mlsanity.com/paper/1603.02501/) (2016)
- [Class-prior Estimation for Learning from Positive and Unlabeled Data](https://mlsanity.com/paper/1611.01586/) (2016)
- [Theoretical Comparisons of Positive-Unlabeled Learning against Positive-Negative Learning](https://mlsanity.com/paper/1603.03130/) (2016)
- [Beyond the Selected Completely At Random Assumption for Learning from Positive and Unlabeled Data](https://mlsanity.com/paper/1809.03207/) (2018)
- [Unbiased Risk Estimators Can Mislead: A Case Study of Learning with Complementary Labels](https://mlsanity.com/paper/2007.02235/) (2020)
- [On Focal Loss for Class-Posterior Probability Estimation: A Theoretical Perspective](https://mlsanity.com/paper/2011.09172/) (2020)
- [A Robust Ensemble Approach to Learn From Positive and Unlabeled Data Using SVM Base Models](https://mlsanity.com/paper/1402.3144/) (2014)
- [Building Classifiers to Predict the Start of Glucose-Lowering Pharmacotherapy Using Belgian Health Expenditure Data](https://mlsanity.com/paper/1504.07389/) (2015)
- [Financial misstatement detection: a realistic evaluation](https://mlsanity.com/paper/2305.17457/) (2023)

## Abstract (arXiv)

We propose a new method of learning from positive and unlabeled (PU) examples in highly imbalanced datasets. Many real-world problems, such as disease gene identification, targeted marketing, fraud detection, and recommender systems, are hard to address with machine learning methods, due to limited labeled data. Often, training data comprises positive and unlabeled instances, the latter typically being dominated by negative, but including also several positive instances. While PU learning is well-studied, few methods address imbalanced settings or hard-to-detect positive examples that resemble negative ones. Our approach uses a focused empirical risk estimator, incorporating both positive and unlabeled examples to train binary classifiers. Empirical evaluations demonstrate state-of-the-art performance on imbalanced datasets under two labeling mechanisms - selecting positives completely at random (SCAR) and selecting at random (SAR). Beyond these controlled experiments, we demonstrate the value of the proposed method in the real-world application of financial misstatement detection.