Mixture Proportion Estimation Beyond Irreducibility

TL;DR

This paper introduces a generalized approach to mixture proportion estimation that relaxes the irreducibility assumption, enabling more flexible and accurate estimation in diverse settings.

Contribution

It proposes a new sufficient condition for MPE and a meta-algorithm that adapts existing methods to this broader context.

Findings

Improved estimation accuracy over baseline methods

Effective adaptation of existing algorithms to new conditions

Empirical validation demonstrating superior performance

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.