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

ArXi:2604.07191v1 Announce Type: new 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 \textit{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.