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arXiv · 2507.05170

Predictive posteriors under hidden confounding

Carlos García Meixide·David Ríos Insua
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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.

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Carlos García Meixide, David Ríos Insua. 2025-07-07. Predictive posteriors under hidden confounding. https://arxiv.org/abs/2507.05170

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