mlsanityData to 14 Oct 2026

Class-prior Estimation for Learning from Positive and Unlabeled Data

arXiv 1611.01586 ↗First posted 5 Nov 2016cs.LG stat.MLcited by 46

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Abstract (arXiv)

We consider the problem of estimating the class prior in an unlabeled dataset. Under the assumption that an additional labeled dataset is available, the class prior can be estimated by fitting a mixture of class-wise data distributions to the unlabeled data distribution. However, in practice, such an additional labeled dataset is often not available. In this paper, we show that, with additional samples coming only from the positive class, the class prior of the unlabeled dataset can be estimated correctly. Our key idea is to use properly penalized divergences for model fitting to cancel the error caused by the absence of negative samples. We further show that the use of the penalized L1-distance gives a computationally efficient algorithm with an analytic solution. The consistency, stability, and estimation error are theoretically analyzed. Finally, we experimentally demonstrate the usefulness of the proposed method.

Key facts. Cited by 46 papers in the map (data through 14 Oct 2026). First posted on arXiv 5 Nov 2016.

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Citing papers per year: 2019: 1; 2020: 0; 2021: 7; 2022: 16; 2023: 4; 2024: 6; 2025: 9; 2026: 3.

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  1. 2022Dist-PU: Positive-Unlabeled Learning from a Label Distribution Perspectivecited by 38
  2. 2019Positive-Unlabeled Reward Learningcited by 37
  3. 2022Adapting to Online Label Shift with Provable Guaranteescited by 26
  4. 2022Learnware: Small Models Do Bigcited by 16
  5. 2021Revisiting the Negative Data of Distantly Supervised Relation Extractioncited by 15
  6. 2022Positive-Unlabeled Learning with Adversarial Data Augmentation for Knowledge Graph Completioncited by 13
  7. 2023Beyond Myopia: Learning from Positive and Unlabeled Data through Holistic Predictive Trendscited by 10
  8. 2022Unsupervised Learning under Latent Label Shiftcited by 9
  9. 2022SPADE: Semi-supervised Anomaly Detection under Distribution Mismatchcited by 9
  10. 2021Quantifying disparities in intimate partner violence: a machine learning method to correct for underreportingcited by 8
  11. 2022Positive Unlabeled Contrastive Learningcited by 8
  12. 2022Positive-Unlabeled Learning using Random Forests via Recursive Greedy Risk Minimizationcited by 8
34 more
  1. 2021Positive-Unlabeled Classification under Class-Prior Shift: A Prior-invariant Approach Based on Density Ratio Estimationcited by 7
  2. 2025Learning from positive and unlabeled examples -Finite size sample boundscited by 6
  3. 2023Robust Positive-Unlabeled Learning via Noise Negative Sample Self-correctioncited by 5
  4. 2021Cell Detection from Imperfect Annotation by Pseudo Label Selection Using P-classificationcited by 3
  5. 2022Uncertainty-aware Pseudo-label Selection for Positive-Unlabeled Learningcited by 3
  6. 2022Positive-Unlabeled Domain Adaptationcited by 3
  7. 2022Double logistic regression approach to biased positive-unlabeled datacited by 3
  8. 2024Offline Reinforcement Learning with Domain-Unlabeled Datacited by 3
  9. 2021LeQua@CLEF2022: Learning to Quantifycited by 2
  10. 2023Leveraging Contaminated Datasets to Learn Clean-Data Distribution with Purified Generative Adversarial Networkscited by 2
  11. 2024Deep Positive-Unlabeled Anomaly Detection for Contaminated Unlabeled Datacited by 2
  12. 2025Positive-Unlabeled Diffusion Models for Preventing Sensitive Data Generationcited by 2
  13. 2021A Novel Perspective for Positive-Unlabeled Learning via Noisy Labelscited by 1
  14. 2021A Positive/Unlabeled Approach for the Segmentation of Medical Sequences using Point-Wise Supervisioncited by 1
  15. 2022Learning from Positive and Unlabeled Data with Augmented Classescited by 1
  16. 2022PU GNN: Chargeback Fraud Detection in P2E MMORPGs via Graph Attention Networks with Imbalanced PU Labelscited by 1
  17. 2022Classification from Positive and Biased Negative Data with Skewed Labeled Posterior Probabilitycited by 0
  18. 2022A Boosting Algorithm for Positive-Unlabeled Learningcited by 0
  19. 2022Learning Acceptance Regions for Many Classes with Anomaly Detectioncited by 0
  20. 2023Regression with Sensor Data Containing Incomplete Observationscited by 0
  21. 2024Soft Label PU Learningcited by 0
  22. 2024MAPL: Memory Augmentation and Pseudo-Labeling for Semi-Supervised Anomaly Detectioncited by 0
  23. 2024PUAL: A Classifier on Trifurcate Positive-Unlabeled Datacited by 0
  24. 2024ESA: Example Sieve Approach for Multi-Positive and Unlabeled Learningcited by 0
  25. 2025Learning from Ambiguous Data with Hard Labelscited by 0
  26. 2025Skill-based Safe Reinforcement Learning with Risk Planningcited by 0
  27. 2025Needles in the Landscape: Semi-Supervised Pseudolabeling for Archaeological Site Discovery under Label Scarcitycited by 0
  28. 2025Cost-Sensitive Unbiased Risk Estimation for Multi-Class Positive-Unlabeled Learningcited by 0
  29. 2025A Unified and Stable Risk Minimization Framework for Weakly Supervised Learning with Theoretical Guaranteescited by 0
  30. 2025Angular Regularization for Positive-Unlabeled Learning on the Hyperspherecited by 0
  31. 2025Sparse classification with positive-confidence data in high dimensionscited by 0
  32. 2026Focused PU learning from imbalanced datacited by 0
  33. 2026How to Mitigate the Distribution Shift Problem in Robotics Control: A Robust and Adaptive Approach Based on Offline to Online Imitation Learningcited by 0
  34. 2026GeoCFM: Positive-Only Conditional Flow Matching for Mineral Occurrence Samplingcited by 0