# Dist-PU: Positive-Unlabeled Learning from a Label Distribution Perspective

arXiv: https://arxiv.org/abs/2212.02801 · HTML: https://mlsanity.com/paper/2212.02801/

## Key facts

- Cited by 38 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 50 references that are in the map.
- First posted on arXiv 6 Dec 2022.

## Builds on (most cited first, 23 of 23)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Exploring the Limits of Transfer Learning with a Unified Text-to-Text Transformer](https://mlsanity.com/paper/1910.10683/) (2019)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [MixMatch: A Holistic Approach to Semi-Supervised Learning](https://mlsanity.com/paper/1905.02249/) (2019)
- [Unsupervised Data Augmentation for Consistency Training](https://mlsanity.com/paper/1904.12848/) (2019)
- [DivideMix: Learning with Noisy Labels as Semi-supervised Learning](https://mlsanity.com/paper/2002.07394/) (2020)
- [Exploring the Limits of Weakly Supervised Pretraining](https://mlsanity.com/paper/1805.00932/) (2018)
- [Deep Learning Scaling is Predictable, Empirically](https://mlsanity.com/paper/1712.00409/) (2017)
- [Pseudo-Labeling and Confirmation Bias in Deep Semi-Supervised Learning](https://mlsanity.com/paper/1908.02983/) (2019)
- [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)
- [Learning with Confident Examples: Rank Pruning for Robust Classification with Noisy Labels](https://mlsanity.com/paper/1705.01936/) (2017)
- [Mixture Proportion Estimation and PU Learning: A Modern Approach](https://mlsanity.com/paper/2111.00980/) (2021)
- [Self-PU: Self Boosted and Calibrated Positive-Unlabeled Training](https://mlsanity.com/paper/2006.11280/) (2020)
- [Class-prior Estimation for Learning from Positive and Unlabeled Data](https://mlsanity.com/paper/1611.01586/) (2016)
- [Classification from Positive, Unlabeled and Biased Negative Data](https://mlsanity.com/paper/1810.00846/) (2018)
- [Positive-unlabeled convolutional neural networks for particle picking in cryo-electron micrographs](https://mlsanity.com/paper/1803.08207/) (2018)
- [Learning from Positive and Unlabeled Data with Arbitrary Positive Shift](https://mlsanity.com/paper/2002.10261/) (2020)
- [Learning Theory and Algorithms for Revenue Optimization in Second-Price Auctions with Reserve](https://mlsanity.com/paper/1310.5665/) (2013)

## Built on by (most cited first, 30 of 38)

- [Feed Two Birds with One Scone: Exploiting Wild Data for Both Out-of-Distribution Generalization and Detection](https://mlsanity.com/paper/2306.09158/) (2023)
- [How Does Unlabeled Data Provably Help Out-of-Distribution Detection?](https://mlsanity.com/paper/2402.03502/) (2024)
- [An Electrocardiogram Foundation Model Built on over 10 Million Recordings with External Evaluation across Multiple Domains](https://mlsanity.com/paper/2410.04133/) (2024)
- [Knowledge-Infused Legal Wisdom: Navigating LLM Consultation through the Lens of Diagnostics and Positive-Unlabeled Reinforcement Learning](https://mlsanity.com/paper/2406.03600/) (2024)
- [Beyond Myopia: Learning from Positive and Unlabeled Data through Holistic Predictive Trends](https://mlsanity.com/paper/2310.04078/) (2023)
- [Learning with Complementary Labels Revisited: The Selected-Completely-at-Random Setting Is More Practical](https://mlsanity.com/paper/2311.15502/) (2023)
- [Harmfully Manipulated Images Matter in Multimodal Misinformation Detection](https://mlsanity.com/paper/2407.19192/) (2024)
- [Class Prior-Free Positive-Unlabeled Learning with Taylor Variational Loss for Hyperspectral Remote Sensing Imagery](https://mlsanity.com/paper/2308.15081/) (2023)
- [A General Framework for Learning from Weak Supervision](https://mlsanity.com/paper/2402.01922/) (2024)
- [Semi-Supervised Disease Classification based on Limited Medical Image Data](https://mlsanity.com/paper/2405.04295/) (2024)
- [Robust Positive-Unlabeled Learning via Noise Negative Sample Self-correction](https://mlsanity.com/paper/2308.00279/) (2023)
- [Community-Based Hierarchical Positive-Unlabeled (PU) Model Fusion for Chronic Disease Prediction](https://mlsanity.com/paper/2309.03386/) (2023)
- [Accurate Link Prediction for Edge-Incomplete Graphs via PU Learning](https://mlsanity.com/paper/2405.11911/) (2024)
- [Dens-PU: PU Learning with Density-Based Positive Labeled Augmentation](https://mlsanity.com/paper/2303.11848/) (2023)
- [A Positive-Unlabeled Metric Learning Framework for Document-Level Relation Extraction with Incomplete Labeling](https://mlsanity.com/paper/2306.14806/) (2023)
- [Positive-Unlabeled Node Classification with Structure-aware Graph Learning](https://mlsanity.com/paper/2310.13538/) (2023)
- [PSPU: Enhanced Positive and Unlabeled Learning by Leveraging Pseudo Supervision](https://mlsanity.com/paper/2407.06698/) (2024)
- [Noise-Resilient Point-wise Anomaly Detection in Time Series Using Weak Segment Labels](https://mlsanity.com/paper/2501.11959/) (2025)
- [ImplicitRM: Unbiased Reward Modeling from Implicit Preference Data for LLM alignment](https://mlsanity.com/paper/2603.23184/) (2026)
- [Zero-Shot Scene Graph Generation via Triplet Calibration and Reduction](https://mlsanity.com/paper/2309.03542/) (2023)
- [Meta-learning for Positive-unlabeled Classification](https://mlsanity.com/paper/2406.03680/) (2024)
- [Medix: Out-of-Distribution Detection from Unlabeled Wild Data via Robust Gradient Statistics](https://mlsanity.com/paper/2510.06505/) (2025)
- [Can Class-Priors Help Single-Positive Multi-Label Learning?](https://mlsanity.com/paper/2309.13886/) (2023)
- [Verifying the Selected Completely at Random Assumption in Positive-Unlabeled Learning](https://mlsanity.com/paper/2404.00145/) (2024)
- [Novel Node Category Detection Under Subpopulation Shift](https://mlsanity.com/paper/2404.01216/) (2024)
- [Prior shift estimation for positive unlabeled data through the lens of kernel embedding](https://mlsanity.com/paper/2502.21194/) (2025)
- [Accessible, Realistic, and Fair Evaluation of Positive-Unlabeled Learning Algorithms](https://mlsanity.com/paper/2509.24228/) (2025)
- [Learning A Disentangling Representation For PU Learning](https://mlsanity.com/paper/2310.03833/) (2023)
- [Adaptive Gradient Calibration for Single-Positive Multi-Label Learning in Remote Sensing Image Scene Classification](https://mlsanity.com/paper/2510.08269/) (2025)
- [Needles in the Landscape: Semi-Supervised Pseudolabeling for Archaeological Site Discovery under Label Scarcity](https://mlsanity.com/paper/2510.16814/) (2025)

## Abstract (arXiv)

Positive-Unlabeled (PU) learning tries to learn binary classifiers from a few labeled positive examples with many unlabeled ones. Compared with ordinary semi-supervised learning, this task is much more challenging due to the absence of any known negative labels. While existing cost-sensitive-based methods have achieved state-of-the-art performances, they explicitly minimize the risk of classifying unlabeled data as negative samples, which might result in a negative-prediction preference of the classifier. To alleviate this issue, we resort to a label distribution perspective for PU learning in this paper. Noticing that the label distribution of unlabeled data is fixed when the class prior is known, it can be naturally used as learning supervision for the model. Motivated by this, we propose to pursue the label distribution consistency between predicted and ground-truth label distributions, which is formulated by aligning their expectations. Moreover, we further adopt the entropy minimization and Mixup regularization to avoid the trivial solution of the label distribution consistency on unlabeled data and mitigate the consequent confirmation bias. Experiments on three benchmark datasets validate the effectiveness of the proposed method.Code available at: https://github.com/Ray-rui/Dist-PU-Positive-Unlabeled-Learning-from-a-Label-Distribution-Perspective.