# Positive-Unlabeled Classification under Class-Prior Shift: A Prior-invariant Approach Based on Density Ratio Estimation

arXiv: https://arxiv.org/abs/2107.05045 · HTML: https://mlsanity.com/paper/2107.05045/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 58 references that are in the map.
- First posted on arXiv 11 Jul 2021.

## Builds on (most cited first, 17 of 17)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Striving for Simplicity: The All Convolutional Net](https://mlsanity.com/paper/1412.6806/) (2014)
- [Deep Learning for Classical Japanese Literature](https://mlsanity.com/paper/1812.01718/) (2018)
- [Size-Independent Sample Complexity of Neural Networks](https://mlsanity.com/paper/1712.06541/) (2017)
- [Positive-Unlabeled Learning with Non-Negative Risk Estimator](https://mlsanity.com/paper/1703.00593/) (2017)
- [Classification with Asymmetric Label Noise: Consistency and Maximal Denoising](https://mlsanity.com/paper/1303.1208/) (2013)
- [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)
- [Non-Negative Bregman Divergence Minimization for Deep Direct Density Ratio Estimation](https://mlsanity.com/paper/2006.06979/) (2020)
- [On the Minimal Supervision for Training Any Binary Classifier from Only Unlabeled Data](https://mlsanity.com/paper/1808.10585/) (2018)
- [Theoretical Comparisons of Positive-Unlabeled Learning against Positive-Negative Learning](https://mlsanity.com/paper/1603.03130/) (2016)
- [Classification from Pairwise Similarity and Unlabeled Data](https://mlsanity.com/paper/1802.04381/) (2018)
- [PU Learning for Matrix Completion](https://mlsanity.com/paper/1411.6081/) (2014)
- [Mitigating Overfitting in Supervised Classification from Two Unlabeled Datasets: A Consistent Risk Correction Approach](https://mlsanity.com/paper/1910.08974/) (2019)
- [Positive-Unlabeled Classification under Class Prior Shift and Asymmetric Error](https://mlsanity.com/paper/1809.07011/) (2018)

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

- [A Unified Positive-Unlabeled Learning Framework for Document-Level Relation Extraction with Different Levels of Labeling](https://mlsanity.com/paper/2210.08709/) (2022)
- [Deep Positive-Unlabeled Anomaly Detection for Contaminated Unlabeled Data](https://mlsanity.com/paper/2405.18929/) (2024)
- [Meta-learning for Positive-unlabeled Classification](https://mlsanity.com/paper/2406.03680/) (2024)
- [Positive-Unlabeled Diffusion Models for Preventing Sensitive Data Generation](https://mlsanity.com/paper/2503.03789/) (2025)
- [Prior shift estimation for positive unlabeled data through the lens of kernel embedding](https://mlsanity.com/paper/2502.21194/) (2025)
- [Improving State-of-the-Art in One-Class Classification by Leveraging Unlabeled Data](https://mlsanity.com/paper/2203.07206/) (2022)
- [A generalized approach to label shift: the Conditional Probability Shift Model](https://mlsanity.com/paper/2503.02583/) (2025)

## Abstract (arXiv)

Learning from positive and unlabeled (PU) data is an important problem in various applications. Most of the recent approaches for PU classification assume that the class-prior (the ratio of positive samples) in the training unlabeled dataset is identical to that of the test data, which does not hold in many practical cases. In addition, we usually do not know the class-priors of the training and test data, thus we have no clue on how to train a classifier without them. To address these problems, we propose a novel PU classification method based on density ratio estimation. A notable advantage of our proposed method is that it does not require the class-priors in the training phase; class-prior shift is incorporated only in the test phase. We theoretically justify our proposed method and experimentally demonstrate its effectiveness.