# Single-sample versus case-control sampling scheme for Positive Unlabeled data: the story of two scenarios

arXiv: https://arxiv.org/abs/2312.02095 · HTML: https://mlsanity.com/paper/2312.02095/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 16 references that are in the map.
- First posted on arXiv 4 Dec 2023.

## Builds on (most cited first, 7 of 7)

- [MiniLM: Deep Self-Attention Distillation for Task-Agnostic Compression of Pre-Trained Transformers](https://mlsanity.com/paper/2002.10957/) (2020)
- [Recommendations as Treatments: Debiasing Learning and Evaluation](https://mlsanity.com/paper/1602.05352/) (2016)
- [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)
- [SwiftFormer: Efficient Additive Attention for Transformer-based Real-time Mobile Vision Applications](https://mlsanity.com/paper/2303.15446/) (2023)
- [Beyond the Selected Completely At Random Assumption for Learning from Positive and Unlabeled Data](https://mlsanity.com/paper/1809.03207/) (2018)
- [On Missing Labels, Long-tails and Propensities in Extreme Multi-label Classification](https://mlsanity.com/paper/2207.13186/) (2022)

## Built on by (most cited first, 1 of 1)

- [Prior shift estimation for positive unlabeled data through the lens of kernel embedding](https://mlsanity.com/paper/2502.21194/) (2025)

## Abstract (arXiv)

In the paper we argue that performance of the classifiers based on Empirical Risk Minimization (ERM) for positive unlabeled data, which are designed for case-control sampling scheme may significantly deteriorate when applied to a single-sample scenario. We reveal why their behavior depends, in all but very specific cases, on the scenario. Also, we introduce a single-sample case analogue of the popular non-negative risk classifier designed for case-control data and compare its performance with the original proposal. We show that the significant differences occur between them, especiall when half or more positive of observations are labeled. The opposite case when ERM minimizer designed for the case-control case is applied for single-sample data is also considered and similar conclusions are drawn. Taking into account difference of scenarios requires a sole, but crucial, change in the definition of the Empirical Risk.