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.

本文提出更一般的充分条件，可以适应不满足不可约性假设的几种设置。进一步提出了一种基于重采样的元算法，可以使任何现有的 MPE 算法适应我们更一般的条件，这种方法在实验中相对于基线方法和最近提出的重组算法展现更好的估计性能。