# Mixture Proportion Estimation via Kernel Embedding of Distributions

arXiv: https://arxiv.org/abs/1603.02501 · HTML: https://mlsanity.com/paper/1603.02501/

## Key facts

- Cited by 67 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Mar 2016.

## Built on by (most cited first, 30 of 67)

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- [Learning with Complementary Labels Revisited: The Selected-Completely-at-Random Setting Is More Practical](https://mlsanity.com/paper/2311.15502/) (2023)
- [Mixture Proportion Estimation Beyond Irreducibility](https://mlsanity.com/paper/2306.01253/) (2023)
- [Quantifying disparities in intimate partner violence: a machine learning method to correct for underreporting](https://mlsanity.com/paper/2110.04133/) (2021)
- [Positive Unlabeled Contrastive Learning](https://mlsanity.com/paper/2206.01206/) (2022)
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- [ZScribbleSeg: Zen and the Art of Scribble Supervised Medical Image Segmentation](https://mlsanity.com/paper/2301.04882/) (2023)
- [Class Prior-Free Positive-Unlabeled Learning with Taylor Variational Loss for Hyperspectral Remote Sensing Imagery](https://mlsanity.com/paper/2308.15081/) (2023)
- [Positive-Unlabeled Classification under Class-Prior Shift: A Prior-invariant Approach Based on Density Ratio Estimation](https://mlsanity.com/paper/2107.05045/) (2021)
- [Self-paced Resistance Learning against Overfitting on Noisy Labels](https://mlsanity.com/paper/2105.03059/) (2021)
- [One-Class Risk Estimation for One-Class Hyperspectral Image Classification](https://mlsanity.com/paper/2210.15457/) (2022)
- [Learning from positive and unlabeled examples -Finite size sample bounds](https://mlsanity.com/paper/2507.07354/) (2025)
- [Robust Offline Imitation Learning from Diverse Auxiliary Data](https://mlsanity.com/paper/2410.03626/) (2024)
- [Making Binary Classification from Multiple Unlabeled Datasets Almost Free of Supervision](https://mlsanity.com/paper/2306.07036/) (2023)
- [Double logistic regression approach to biased positive-unlabeled data](https://mlsanity.com/paper/2209.07787/) (2022)
- [Positive and Unlabeled Data: Model, Estimation, Inference, and Classification](https://mlsanity.com/paper/2407.09735/) (2024)
- [Rethinking Consistent Multi-Label Classification Under Inexact Supervision](https://mlsanity.com/paper/2510.04091/) (2025)
- [Leveraging Contaminated Datasets to Learn Clean-Data Distribution with Purified Generative Adversarial Networks](https://mlsanity.com/paper/2302.01722/) (2023)
- [Binary Classification with Instance and Label Dependent Label Noise](https://mlsanity.com/paper/2306.03402/) (2023)
- [A Generalized Unbiased Risk Estimator for Learning with Augmented Classes](https://mlsanity.com/paper/2306.06894/) (2023)

## 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.