# Mixture Proportion Estimation Beyond Irreducibility

arXiv: https://arxiv.org/abs/2306.01253 · HTML: https://mlsanity.com/paper/2306.01253/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 42 references that are in the map.
- First posted on arXiv 2 Jun 2023.

## Builds on (most cited first, 12 of 12)

- [Positive-Unlabeled Learning with Non-Negative Risk Estimator](https://mlsanity.com/paper/1703.00593/) (2017)
- [Learning from positive and unlabeled data: a survey](https://mlsanity.com/paper/1811.04820/) (2018)
- [Mixture Proportion Estimation via Kernel Embedding of Distributions](https://mlsanity.com/paper/1603.02501/) (2016)
- [Transfer Learning for Nonparametric Classification: Minimax Rate and Adaptive Classifier](https://mlsanity.com/paper/1906.02903/) (2019)
- [Mixture Proportion Estimation and PU Learning: A Modern Approach](https://mlsanity.com/paper/2111.00980/) (2021)
- [Beyond the Selected Completely At Random Assumption for Learning from Positive and Unlabeled Data](https://mlsanity.com/paper/1809.03207/) (2018)
- [A Generalized Neyman-Pearson Criterion for Optimal Domain Adaptation](https://mlsanity.com/paper/1810.01545/) (2018)
- [A linear adjustment based approach to posterior drift in transfer learning](https://mlsanity.com/paper/2111.10841/) (2021)
- [Rethinking Class-Prior Estimation for Positive-Unlabeled Learning](https://mlsanity.com/paper/2002.03673/) (2020)
- [Nonparametric semi-supervised learning of class proportions](https://mlsanity.com/paper/1601.01944/) (2016)
- [Quantifying disparities in intimate partner violence: a machine learning method to correct for underreporting](https://mlsanity.com/paper/2110.04133/) (2021)
- [Class Proportion Estimation with Application to Multiclass Anomaly Rejection](https://mlsanity.com/paper/1306.5056/) (2013)

## Built on by (most cited first, 9 of 9)

- [Label-Noise Robust Diffusion Models](https://mlsanity.com/paper/2402.17517/) (2024)
- [Robust Offline Imitation Learning from Diverse Auxiliary Data](https://mlsanity.com/paper/2410.03626/) (2024)
- [Rethinking Consistent Multi-Label Classification Under Inexact Supervision](https://mlsanity.com/paper/2510.04091/) (2025)
- [Unraveling the Impact of Heterophilic Structures on Graph Positive-Unlabeled Learning](https://mlsanity.com/paper/2405.19919/) (2024)
- [Conformal Data Contamination Tests for In-distribution Data Acquisition](https://mlsanity.com/paper/2507.13835/) (2025)
- [Accessible, Realistic, and Fair Evaluation of Positive-Unlabeled Learning Algorithms](https://mlsanity.com/paper/2509.24228/) (2025)
- [Semiparametric Learning from Open-Set Label Shift Data](https://mlsanity.com/paper/2509.14522/) (2025)
- [Mixture Proportion Estimation and Weakly-supervised Kernel Test for Conditional Independence](https://mlsanity.com/paper/2604.07191/) (2026)
- [Estimation of the Label-Noise Transition Matrix with Performance Guarantees via Selective Classification](https://mlsanity.com/paper/2609.39829/) (2026)

## Abstract (arXiv)

The task of mixture proportion estimation (MPE) is to estimate the weight of a component distribution in a mixture, given observations from both the component and mixture. Previous work on MPE adopts the irreducibility assumption, which ensures identifiablity of the mixture proportion. In this paper, we propose a more general sufficient condition that accommodates several settings of interest where irreducibility does not hold. We further present a resampling-based meta-algorithm that takes any existing MPE algorithm designed to work under irreducibility and adapts it to work under our more general condition. Our approach empirically exhibits improved estimation performance relative to baseline methods and to a recently proposed regrouping-based algorithm.