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

Yushi Hirose, Akito Narahara, Takafumi Kanamori
Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, PMLR 300:694-702, 2026.

Abstract

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 \emph{irreducibility} 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v300-hirose26a, title = { Mixture Proportion Estimation and Weakly-supervised Kernel Test for Conditional Independence }, author = {Hirose, Yushi and Narahara, Akito and Kanamori, Takafumi}, booktitle = {Proceedings of The 29th International Conference on Artificial Intelligence and Statistics}, pages = {694--702}, year = {2026}, editor = {Khan, Emtiyaz and Li, Yingzhen and Solin, Arno and Ramdas, Aaditya}, volume = {300}, series = {Proceedings of Machine Learning Research}, month = {02--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v300/main/assets/hirose26a/hirose26a.pdf}, url = {https://proceedings.mlr.press/v300/hirose26a.html}, abstract = { 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 \emph{irreducibility} 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. } }
Endnote
%0 Conference Paper %T Mixture Proportion Estimation and Weakly-supervised Kernel Test for Conditional Independence %A Yushi Hirose %A Akito Narahara %A Takafumi Kanamori %B Proceedings of The 29th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2026 %E Emtiyaz Khan %E Yingzhen Li %E Arno Solin %E Aaditya Ramdas %F pmlr-v300-hirose26a %I PMLR %P 694--702 %U https://proceedings.mlr.press/v300/hirose26a.html %V 300 %X 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 \emph{irreducibility} 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.
APA
Hirose, Y., Narahara, A. & Kanamori, T.. (2026). Mixture Proportion Estimation and Weakly-supervised Kernel Test for Conditional Independence . Proceedings of The 29th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 300:694-702 Available from https://proceedings.mlr.press/v300/hirose26a.html.

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