# Mixture Proportion Estimation and Weakly-supervised Kernel Test for Conditional Independence

arXiv: https://arxiv.org/abs/2604.07191 · HTML: https://mlsanity.com/paper/2604.07191/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 53 references that are in the map.
- First posted on arXiv 8 Apr 2026.

## Builds on (most cited first, 22 of 22)

- [A Survey on Bias and Fairness in Machine Learning](https://mlsanity.com/paper/1908.09635/) (2019)
- [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)
- [Classification with Asymmetric Label Noise: Consistency and Maximal Denoising](https://mlsanity.com/paper/1303.1208/) (2013)
- [Mixture Proportion Estimation via Kernel Embedding of Distributions](https://mlsanity.com/paper/1603.02501/) (2016)
- [On the Minimal Supervision for Training Any Binary Classifier from Only Unlabeled Data](https://mlsanity.com/paper/1808.10585/) (2018)
- [Classification from Pairwise Similarity and Unlabeled Data](https://mlsanity.com/paper/1802.04381/) (2018)
- [Domain Adaptation under Open Set Label Shift](https://mlsanity.com/paper/2207.13048/) (2022)
- [Efficient Conditionally Invariant Representation Learning](https://mlsanity.com/paper/2212.08645/) (2022)
- [Unsupervised Risk Estimation Using Only Conditional Independence Structure](https://mlsanity.com/paper/1606.05313/) (2016)
- [Rethinking Class-Prior Estimation for Positive-Unlabeled Learning](https://mlsanity.com/paper/2002.03673/) (2020)
- [Practical Kernel Tests of Conditional Independence](https://mlsanity.com/paper/2402.13196/) (2024)
- [Nonparametric semi-supervised learning of class proportions](https://mlsanity.com/paper/1601.01944/) (2016)
- [A Practical Introduction to Kernel Discrepancies: MMD, HSIC & KSD](https://mlsanity.com/paper/2503.04820/) (2025)
- [Binary Classification from Multiple Unlabeled Datasets via Surrogate Set Classification](https://mlsanity.com/paper/2102.00678/) (2021)
- [A simpler condition for consistency of a kernel independence test](https://mlsanity.com/paper/1501.06103/) (2015)
- [Causal Inference Despite Limited Global Confounding via Mixture Models](https://mlsanity.com/paper/2112.11602/) (2021)
- [Mixture Proportion Estimation Beyond Irreducibility](https://mlsanity.com/paper/2306.01253/) (2023)
- [Nonparametric Estimation of Multi-View Latent Variable Models](https://mlsanity.com/paper/1311.3287/) (2013)
- [Class Proportion Estimation with Application to Multiclass Anomaly Rejection](https://mlsanity.com/paper/1306.5056/) (2013)
- [Causal Discovery in Mixtures of Populations](https://mlsanity.com/paper/2311.07454/) (2023)
- [Causal Discovery via Conditional Independence Testing with Proxy Variables](https://mlsanity.com/paper/2305.05281/) (2023)

## Abstract (arXiv)

Mixture proportion estimation (MPE) aims to estimate class priors from unlabeled data. This task is a critical component in weakly supervised learning, such as PU learning, learning with label noise, and domain adaptation. Existing MPE methods rely on the textitirreducibility assumption or its variant for identifiability. In this paper, we propose novel assumptions based on conditional independence (CI) given the class label, which ensure identifiability even when irreducibility does not hold. We develop method of moments estimators under these assumptions and analyze their asymptotic properties. Furthermore, we present weakly-supervised kernel tests to validate the CI assumptions, which are of independent interest in applications such as causal discovery and fairness evaluation. Empirically, we demonstrate the improved performance of our estimators compared with existing methods and that our tests successfully control both type I and type II errors.labelkey