Mixture Proportion Estimation Beyond Irreducibility

Yilun Zhu, Aaron Fjeldsted, Darren Holland, George Landon, Azaree Lintereur, Clayton Scott
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:42962-42982, 2023.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-zhu23c, title = {Mixture Proportion Estimation Beyond Irreducibility}, author = {Zhu, Yilun and Fjeldsted, Aaron and Holland, Darren and Landon, George and Lintereur, Azaree and Scott, Clayton}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {42962--42982}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/zhu23c/zhu23c.pdf}, url = {https://proceedings.mlr.press/v202/zhu23c.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Mixture Proportion Estimation Beyond Irreducibility %A Yilun Zhu %A Aaron Fjeldsted %A Darren Holland %A George Landon %A Azaree Lintereur %A Clayton Scott %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-zhu23c %I PMLR %P 42962--42982 %U https://proceedings.mlr.press/v202/zhu23c.html %V 202 %X 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.
APA
Zhu, Y., Fjeldsted, A., Holland, D., Landon, G., Lintereur, A. & Scott, C.. (2023). Mixture Proportion Estimation Beyond Irreducibility. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:42962-42982 Available from https://proceedings.mlr.press/v202/zhu23c.html.

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