Predictive posteriors under hidden confounding

TL;DR

This paper introduces a Bayesian framework for predictive modeling under hidden confounding that provides well-calibrated uncertainty estimates and improves with more data, demonstrated through simulations and medical applications.

Contribution

The paper presents a novel Bayesian approach that offers principled uncertainty quantification and better posterior contraction rates in the presence of hidden confounders.

Findings

Achieves well-calibrated predictive distributions across domains

Maintains high empirical coverage in various settings

Improves posterior contraction rates with more datasets

Abstract

Predicting outcomes in external domains is challenging due to hidden confounders that potentially influence both predictors and outcomes. Well-established methods frequently rely on stringent assumptions, explicit knowledge about the distribution shift across domains, or bias-inducing regularization schemes to enhance generalization. While recent developments in point prediction under hidden confounding attempt to mitigate these shortcomings, they generally do not provide principled uncertainty quantification. We introduce a Bayesian framework that yields well-calibrated predictive distributions across external domains, supports valid model inference, and achieves posterior contraction rates that improve as the number of observed datasets increases. Simulations and a medical application highlight the remarkable empirical coverage of our approach, nearly unchanged when transitioning from low- to moderate-dimensional settings.