Unsupervised domain adaptation under hidden confounding

Abstract: We introduce a new predictive mechanism that operates in the presence of hidden confounding across distributionally diverse data sources while ensuring consistent estimation of causal parameters-despite their recognized suboptimality for prediction in the literature. Our method is based on a novel estimand that captures the dependence structure between response noise and covariates, incorporating causal parameters into a generative model that adaptively replicates the conditional distribution of the test environment. Identifiability is achieved under a straightforward, empirically verifiable assumption. Our approach ensures probabilistic alignment with test distributions uniformly across arbitrary interventions, enabling valid predictions without requiring worst-case optimization or assumptions about the strength of perturbations at test time. Through extensive simulations, we demonstrate that our method outperforms state-of-the-art invariance-based and domain adaptation approaches. Additionally, we validate its practical applicability and superior target risk performance on a cardiovascular disease dataset.