Mixture Proportion Estimation and Weakly-supervised Kernel Test for Conditional Independence
This work addresses a critical bottleneck in weakly supervised learning for applications like PU learning and domain adaptation, offering a novel approach with empirical gains.
The paper tackles the problem of mixture proportion estimation (MPE) by proposing new assumptions based on conditional independence to ensure identifiability when traditional irreducibility fails, and demonstrates improved estimator performance and effective kernel tests for validation.
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. We develop method of moments estimators under these assumptions and analyze their asymptotic properties. Furthermore, we present weakly-supervised kernel tests to validate the CI assumptions, which are of independent interest in applications such as causal discovery and fairness evaluation. Empirically, we demonstrate the improved performance of our estimators compared with existing methods and that our tests successfully control both type I and type II errors.\label{key}