mlsanityData to 7 Oct 2026

Theoretical Comparisons of Positive-Unlabeled Learning against Positive-Negative Learning

arXiv 1603.03130 ↗First posted 10 Mar 2016cs.LG stat.MLcited by 41

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Abstract (arXiv)

In PU learning, a binary classifier is trained from positive (P) and unlabeled (U) data without negative (N) data. Although N data is missing, it sometimes outperforms PN learning (i.e., ordinary supervised learning). Hitherto, neither theoretical nor experimental analysis has been given to explain this phenomenon. In this paper, we theoretically compare PU (and NU) learning against PN learning based on the upper bounds on estimation errors. We find simple conditions when PU and NU learning are likely to outperform PN learning, and we prove that, in terms of the upper bounds, either PU or NU learning (depending on the class-prior probability and the sizes of P and N data) given infinite U data will improve on PN learning. Our theoretical findings well agree with the experimental results on artificial and benchmark data even when the experimental setup does not match the theoretical assumptions exactly.

Key facts. Cited by 41 papers in the map (data through 7 Oct 2026). First posted on arXiv 10 Mar 2016.

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Citing papers per year: 2019: 1; 2020: 0; 2021: 6; 2022: 4; 2023: 8; 2024: 7; 2025: 10; 2026: 5.

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  1. 2023Feed Two Birds with One Scone: Exploiting Wild Data for Both Out-of-Distribution Generalization and Detectioncited by 57
  2. 2019Positive-Unlabeled Reward Learningcited by 36
  3. 2024How Does Unlabeled Data Provably Help Out-of-Distribution Detection?cited by 36
  4. 2021Meta Discovery: Learning to Discover Novel Classes given Very Limited Datacited by 30
  5. 2021Learning Bounds for Open-Set Learningcited by 27
  6. 2023Compete to Win: Enhancing Pseudo Labels for Barely-supervised Medical Image Segmentationcited by 10
  7. 2023Learning with Complementary Labels Revisited: The Selected-Completely-at-Random Setting Is More Practicalcited by 10
  8. 2022Positive Unlabeled Contrastive Learningcited by 8
  9. 2021Positive-Unlabeled Classification under Class-Prior Shift: A Prior-invariant Approach Based on Density Ratio Estimationcited by 7
  10. 2025Learning from positive and unlabeled examples -Finite size sample boundscited by 6
  11. 2023Unified Risk Analysis for Weakly Supervised Learningcited by 5
  12. 2025Out-of-Distribution Detection using Synthetic Data Generationcited by 4
29 more
  1. 2026Positive-Unlabeled Reinforcement Learning Distillation for On-Premise Small Modelscited by 4
  2. 2021The Computational Drug Repositioning without Negative Samplingcited by 3
  3. 2023Unlabeled Imperfect Demonstrations in Adversarial Imitation Learningcited by 3
  4. 2023Partial-Label Regressioncited by 3
  5. 2024Lambda: Learning Matchable Prior For Entity Alignment with Unlabeled Dangling Casescited by 3
  6. 2024PSPU: Enhanced Positive and Unlabeled Learning by Leveraging Pseudo Supervisioncited by 3
  7. 2023Anomaly detection with semi-supervised classification based on risk estimatorscited by 2
  8. 2024Deep Positive-Unlabeled Anomaly Detection for Contaminated Unlabeled Datacited by 2
  9. 2024Unraveling the Impact of Heterophilic Structures on Graph Positive-Unlabeled Learningcited by 2
  10. 2025Medix: Out-of-Distribution Detection from Unlabeled Wild Data via Robust Gradient Statisticscited by 2
  11. 2022Learning from Positive and Unlabeled Data with Augmented Classescited by 1
  12. 2023Automatic Debiased Learning from Positive, Unlabeled, and Exposure Datacited by 1
  13. 2025Accessible, Realistic, and Fair Evaluation of Positive-Unlabeled Learning Algorithmscited by 1
  14. 2021A Symmetric Loss Perspective of Reliable Machine Learningcited by 0
  15. 2021Active Refinement for Multi-Label Learning: A Pseudo-Label Approachcited by 0
  16. 2022Improving State-of-the-Art in One-Class Classification by Leveraging Unlabeled Datacited by 0
  17. 2022A Boosting Algorithm for Positive-Unlabeled Learningcited by 0
  18. 2024Document Set Expansion with Positive-Unlabeled Learning: A Density Estimation-based Approachcited by 0
  19. 2024Learning from Concealed Labelscited by 0
  20. 2025Learning from Ambiguous Data with Hard Labelscited by 0
  21. 2025Detecting Scarce and Sparse Anomalous: Solving Dual Imbalance in Multi-Instance Learningcited by 0
  22. 2025Learning from Double Positive and Unlabeled Data for Potential-Customer Identificationcited by 0
  23. 2025A deep multiple instance learning approach based on coarse labels for high-resolution land-cover mappingcited by 0
  24. 2025Adaptive Gradient Calibration for Single-Positive Multi-Label Learning in Remote Sensing Image Scene Classificationcited by 0
  25. 2025Semi-Supervised Treatment Effect Estimation with Unlabeled Covariates for Prediction-Powered Causal Inferencecited by 0
  26. 2026Learning from Label Proportions with Dual-proportion Constraintscited by 0
  27. 2026Focused PU learning from imbalanced datacited by 0
  28. 2026Generalized Distribution-Free Semi-Supervised Learning with Risk Rewritecited by 0
  29. 2026Positive-Unlabeled Preference Optimization For Chest X-ray Report Generationcited by 0