mlsanityData to 7 Oct 2026

Positive-Unlabeled Learning with Non-Negative Risk Estimator

arXiv 1703.00593 ↗First posted 2 Mar 2017cs.LG stat.MLcited by 217

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Abstract (arXiv)

From only positive (P) and unlabeled (U) data, a binary classifier could be trained with PU learning, in which the state of the art is unbiased PU learning. However, if its model is very flexible, empirical risks on training data will go negative, and we will suffer from serious overfitting. In this paper, we propose a non-negative risk estimator for PU learning: when getting minimized, it is more robust against overfitting, and thus we are able to use very flexible models (such as deep neural networks) given limited P data. Moreover, we analyze the bias, consistency, and mean-squared-error reduction of the proposed risk estimator, and bound the estimation error of the resulting empirical risk minimizer. Experiments demonstrate that our risk estimator fixes the overfitting problem of its unbiased counterparts.

Key facts. Cited by 217 papers in the map (data through 7 Oct 2026). First posted on arXiv 2 Mar 2017.

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Citing papers per year: 2019: 2; 2020: 2; 2021: 27; 2022: 30; 2023: 36; 2024: 36; 2025: 40; 2026: 44.

217 papers.

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  2. 2019Imitation Learning from Imperfect Demonstrationcited by 112
  3. 2022Is Out-of-Distribution Detection Learnable?cited by 109
  4. 2020Offline Learning from Demonstrations and Unlabeled Experiencecited by 72
  5. 2023Multiscale Positive-Unlabeled Detection of AI-Generated Textscited by 59
  6. 2021Mixture Proportion Estimation and PU Learning: A Modern Approachcited by 52
  7. 2022Dist-PU: Positive-Unlabeled Learning from a Label Distribution Perspectivecited by 37
  8. 2019Positive-Unlabeled Reward Learningcited by 36
  9. 2022Domain Adaptation under Open Set Label Shiftcited by 32
  10. 2021Meta Discovery: Learning to Discover Novel Classes given Very Limited Datacited by 30
  11. 2022ShapePU: A New PU Learning Framework Regularized by Global Consistency for Scribble Supervised Cardiac Segmentationcited by 26
  12. 2020Semi-supervised reward learning for offline reinforcement learningcited by 22
38 more
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  4. 2025Early Stopping Against Label Noise Without Validation Datacited by 21
  5. 2021Learning from Similarity-Confidence Datacited by 19
  6. 2025HyperFree: A Channel-adaptive and Tuning-free Foundation Model for Hyperspectral Remote Sensing Imagerycited by 16
  7. 2024A Short Survey on Importance Weighting for Machine Learningcited by 15
  8. 2022Positive-Unlabeled Learning with Adversarial Data Augmentation for Knowledge Graph Completioncited by 13
  9. 2021Tackling Instance-Dependent Label Noise via a Universal Probabilistic Modelcited by 12
  10. 2021GreedyNASv2: Greedier Search with a Greedy Path Filtercited by 12
  11. 2022AHP: Learning to Negative Sample for Hyperedge Predictioncited by 12
  12. 2024Knowledge-Infused Legal Wisdom: Navigating LLM Consultation through the Lens of Diagnostics and Positive-Unlabeled Reinforcement Learningcited by 12
  13. 2024Decoupling the Class Label and the Target Concept in Machine Unlearningcited by 12
  14. 2021Learning Graph Neural Networks with Positive and Unlabeled Nodescited by 11
  15. 2023Weakly Supervised AUC Optimization: A Unified Partial AUC Approachcited by 11
  16. 2021Federated Learning with Positive and Unlabeled Datacited by 10
  17. 2022Fairness-aware Model-agnostic Positive and Unlabeled Learningcited by 10
  18. 2023Compete to Win: Enhancing Pseudo Labels for Barely-supervised Medical Image Segmentationcited by 10
  19. 2023Learning with Complementary Labels Revisited: The Selected-Completely-at-Random Setting Is More Practicalcited by 10
  20. 2021Positive-unlabeled Learning for Cell Detection in Histopathology Images with Incomplete Annotationscited by 9
  21. 2022A Unified Positive-Unlabeled Learning Framework for Document-Level Relation Extraction with Different Levels of Labelingcited by 9
  22. 2023Mixture Proportion Estimation Beyond Irreducibilitycited by 9
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  24. 2023A Unified Approach to Count-Based Weakly-Supervised Learningcited by 9
  25. 2021Weak Adaptation Learning -- Addressing Cross-domain Data Insufficiency with Weak Annotatorcited by 8
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  27. 2022Positive-Unlabeled Learning using Random Forests via Recursive Greedy Risk Minimizationcited by 8
  28. 2023ZScribbleSeg: Zen and the Art of Scribble Supervised Medical Image Segmentationcited by 8
  29. 2023Improving Behavioural Cloning with Positive Unlabeled Learningcited by 8
  30. 2023When Less is Enough: Positive and Unlabeled Learning Model for Vulnerability Detectioncited by 8
  31. 2023Class Prior-Free Positive-Unlabeled Learning with Taylor Variational Loss for Hyperspectral Remote Sensing Imagerycited by 8
  32. 2021Positive-Unlabeled Classification under Class-Prior Shift: A Prior-invariant Approach Based on Density Ratio Estimationcited by 7
  33. 2023Positive Label Is All You Need for Multi-Label Classificationcited by 7
  34. 2024A General Framework for Learning from Weak Supervisioncited by 7
  35. 2024Semi-Supervised Disease Classification based on Limited Medical Image Datacited by 7
  36. 2021Meta-Learning for Relative Density-Ratio Estimationcited by 6
  37. 2022Multi-class Classification from Multiple Unlabeled Datasets with Partial Risk Regularizationcited by 6
  38. 2023Federated Learning under Covariate Shifts with Generalization Guaranteescited by 6

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