# Positive-Unlabeled Classification under Class Prior Shift and Asymmetric Error

arXiv: https://arxiv.org/abs/1809.07011 · HTML: https://mlsanity.com/paper/1809.07011/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Sep 2018.

## Built on by (most cited first, 7 of 7)

- [From Concept Drift to Model Degradation: An Overview on Performance-Aware Drift Detectors](https://mlsanity.com/paper/2203.11070/) (2022)
- [A Unified Positive-Unlabeled Learning Framework for Document-Level Relation Extraction with Different Levels of Labeling](https://mlsanity.com/paper/2210.08709/) (2022)
- [Positive-Unlabeled Classification under Class-Prior Shift: A Prior-invariant Approach Based on Density Ratio Estimation](https://mlsanity.com/paper/2107.05045/) (2021)
- [Meta-learning for Positive-unlabeled Classification](https://mlsanity.com/paper/2406.03680/) (2024)
- [TTM-RE: Memory-Augmented Document-Level Relation Extraction](https://mlsanity.com/paper/2406.05906/) (2024)
- [A Symmetric Loss Perspective of Reliable Machine Learning](https://mlsanity.com/paper/2101.01366/) (2021)
- [Improving State-of-the-Art in One-Class Classification by Leveraging Unlabeled Data](https://mlsanity.com/paper/2203.07206/) (2022)

## Abstract (arXiv)

Bottlenecks of binary classification from positive and unlabeled data (PU classification) are the requirements that given unlabeled patterns are drawn from the test marginal distribution, and the penalty of the false positive error is identical to the false negative error. However, such requirements are often not fulfilled in practice. In this paper, we generalize PU classification to the class prior shift and asymmetric error scenarios. Based on the analysis of the Bayes optimal classifier, we show that given a test class prior, PU classification under class prior shift is equivalent to PU classification with asymmetric error. Then, we propose two different frameworks to handle these problems, namely, a risk minimization framework and density ratio estimation framework. Finally, we demonstrate the effectiveness of the proposed frameworks and compare both frameworks through experiments using benchmark datasets.