mlsanityData to 7 Oct 2026

Mixture Proportion Estimation via Kernel Embedding of Distributions

arXiv 1603.02501 ↗First posted 8 Mar 2016cs.LG stat.MLcited by 67

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Abstract (arXiv)

Mixture proportion estimation (MPE) is the problem of estimating the weight of a component distribution in a mixture, given samples from the mixture and component. This problem constitutes a key part in many "weakly supervised learning" problems like learning with positive and unlabelled samples, learning with label noise, anomaly detection and crowdsourcing. While there have been several methods proposed to solve this problem, to the best of our knowledge no efficient algorithm with a proven convergence rate towards the true proportion exists for this problem. We fill this gap by constructing a provably correct algorithm for MPE, and derive convergence rates under certain assumptions on the distribution. Our method is based on embedding distributions onto an RKHS, and implementing it only requires solving a simple convex quadratic programming problem a few times. We run our algorithm on several standard classification datasets, and demonstrate that it performs comparably to or better than other algorithms on most datasets.

Key facts. Cited by 67 papers in the map (data through 7 Oct 2026). First posted on arXiv 8 Mar 2016.

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Citing papers per year: 2021: 8; 2022: 13; 2023: 11; 2024: 9; 2025: 13; 2026: 13.

67 papers.

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  1. 2021To Smooth or Not? When Label Smoothing Meets Noisy Labelscited by 70
  2. 2021Learning Noise Transition Matrix from Only Noisy Labels via Total Variation Regularizationcited by 62
  3. 2021Mixture Proportion Estimation and PU Learning: A Modern Approachcited by 52
  4. 2022Dist-PU: Positive-Unlabeled Learning from a Label Distribution Perspectivecited by 37
  5. 2021Unsupervised Domain Adaptation of Black-Box Source Modelscited by 32
  6. 2022Domain Adaptation under Open Set Label Shiftcited by 32
  7. 2022ShapePU: A New PU Learning Framework Regularized by Global Consistency for Scribble Supervised Cardiac Segmentationcited by 26
  8. 2022Adapting to Online Label Shift with Provable Guaranteescited by 26
  9. 2022Learnware: Small Models Do Bigcited by 16
  10. 2024Label-Noise Robust Diffusion Modelscited by 16
  11. 2023Learning with Complementary Labels Revisited: The Selected-Completely-at-Random Setting Is More Practicalcited by 10
  12. 2023Mixture Proportion Estimation Beyond Irreducibilitycited by 9
38 more
  1. 2023Beyond Myopia: Learning from Positive and Unlabeled Data through Holistic Predictive Trendscited by 9
  2. 2021Quantifying disparities in intimate partner violence: a machine learning method to correct for underreportingcited by 8
  3. 2022Positive Unlabeled Contrastive Learningcited by 8
  4. 2022Positive-Unlabeled Learning using Random Forests via Recursive Greedy Risk Minimizationcited by 8
  5. 2023ZScribbleSeg: Zen and the Art of Scribble Supervised Medical Image Segmentationcited by 8
  6. 2023Class Prior-Free Positive-Unlabeled Learning with Taylor Variational Loss for Hyperspectral Remote Sensing Imagerycited by 8
  7. 2021Positive-Unlabeled Classification under Class-Prior Shift: A Prior-invariant Approach Based on Density Ratio Estimationcited by 7
  8. 2021Self-paced Resistance Learning against Overfitting on Noisy Labelscited by 6
  9. 2022One-Class Risk Estimation for One-Class Hyperspectral Image Classificationcited by 6
  10. 2025Learning from positive and unlabeled examples -Finite size sample boundscited by 6
  11. 2023Making Binary Classification from Multiple Unlabeled Datasets Almost Free of Supervisioncited by 4
  12. 2024Robust Offline Imitation Learning from Diverse Auxiliary Datacited by 4
  13. 2022Double logistic regression approach to biased positive-unlabeled datacited by 3
  14. 2024Positive and Unlabeled Data: Model, Estimation, Inference, and Classificationcited by 3
  15. 2025Rethinking Consistent Multi-Label Classification Under Inexact Supervisioncited by 3
  16. 2023Leveraging Contaminated Datasets to Learn Clean-Data Distribution with Purified Generative Adversarial Networkscited by 2
  17. 2023Binary Classification with Instance and Label Dependent Label Noisecited by 2
  18. 2023A Generalized Unbiased Risk Estimator for Learning with Augmented Classescited by 2
  19. 2024Deep Positive-Unlabeled Anomaly Detection for Contaminated Unlabeled Datacited by 2
  20. 2024Unraveling the Impact of Heterophilic Structures on Graph Positive-Unlabeled Learningcited by 2
  21. 2024Meta-learning for Positive-unlabeled Classificationcited by 2
  22. 2025Positive-Unlabeled Diffusion Models for Preventing Sensitive Data Generationcited by 2
  23. 2021A Novel Perspective for Positive-Unlabeled Learning via Noisy Labelscited by 1
  24. 2022Learning from Positive and Unlabeled Data with Augmented Classescited by 1
  25. 2024Verifying the Selected Completely at Random Assumption in Positive-Unlabeled Learningcited by 1
  26. 2025Weakly-Supervised Contrastive Learning for Imprecise Class Labelscited by 1
  27. 2025Conformal Data Contamination Tests for In-distribution Data Acquisitioncited by 1
  28. 2025Accessible, Realistic, and Fair Evaluation of Positive-Unlabeled Learning Algorithmscited by 1
  29. 2026SMI: Statistical Membership Inference for Reliable Unlearned Model Auditingcited by 1
  30. 2026Hitting a Moving Target: Test-Time Adaptation for AI Text Detection under Continual Distribution Shiftcited by 1
  31. 2022Risk bounds for PU learning under Selected At Random assumptioncited by 0
  32. 2022A Boosting Algorithm for Positive-Unlabeled Learningcited by 0
  33. 2022Complementary Labels Learning with Augmented Classescited by 0
  34. 2023Positive Unlabeled Learning Selected Not At Random (PULSNAR): class proportion estimation when the SCAR assumption does not holdcited by 0
  35. 2023Regression with Sensor Data Containing Incomplete Observationscited by 0
  36. 2024An Unbiased Risk Estimator for Partial Label Learning with Augmented Classescited by 0
  37. 2024ESA: Example Sieve Approach for Multi-Positive and Unlabeled Learningcited by 0
  38. 2025Prior shift estimation for positive unlabeled data through the lens of kernel embeddingcited by 0

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