# Augmented prediction of a true class for Positive Unlabeled data under selection bias

arXiv: https://arxiv.org/abs/2407.10309 · HTML: https://mlsanity.com/paper/2407.10309/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 23 references that are in the map.
- First posted on arXiv 14 Jul 2024.

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

- [Deep Learning Recommendation Model for Personalization and Recommendation Systems](https://mlsanity.com/paper/1906.00091/) (2019)
- [Recommendations as Treatments: Debiasing Learning and Evaluation](https://mlsanity.com/paper/1602.05352/) (2016)
- [Learning from positive and unlabeled data: a survey](https://mlsanity.com/paper/1811.04820/) (2018)
- [Beyond the Selected Completely At Random Assumption for Learning from Positive and Unlabeled Data](https://mlsanity.com/paper/1809.03207/) (2018)
- [Structured Prediction with Partial Labelling through the Infimum Loss](https://mlsanity.com/paper/2003.00920/) (2020)
- [On Missing Labels, Long-tails and Propensities in Extreme Multi-label Classification](https://mlsanity.com/paper/2207.13186/) (2022)

## Abstract (arXiv)

We introduce a new observational setting for Positive Unlabeled (PU) data where the observations at prediction time are also labeled. This occurs commonly in practice -- we argue that the additional information is important for prediction, and call this task "augmented PU prediction". We allow for labeling to be feature dependent. In such scenario, Bayes classifier and its risk is established and compared with a risk of a classifier which for unlabeled data is based only on predictors. We introduce several variants of the empirical Bayes rule in such scenario and investigate their performance. We emphasise dangers (and ease) of applying classical classification rule in the augmented PU scenario -- due to no preexisting studies, an unaware researcher is prone to skewing the obtained predictions. We conclude that the variant based on recently proposed variational autoencoder designed for PU scenario works on par or better than other considered variants and yields advantage over feature-only based methods in terms of accuracy for unlabeled samples.