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.

翻译：混合比例估计（MPE）任务旨在根据来自成分分布与混合分布的观测数据，估计混合分布中某一成分分布的权重。先前关于MPE的研究均采用不可约性假设，该假设确保了混合比例的可识别性。本文提出了一种更广义的充分条件，该条件适用于不可约性不成立的若干重要场景。我们进一步提出了一种基于重采样的元算法，该算法能够将任何现有依赖于不可约性假设的MPE算法适配至本文提出的更广义条件下工作。实验表明，与基线方法及近期提出的基于重分组算法相比，我们的方法在估计性能上取得了改进。