Predictive posteriors under hidden confounding

2025/07/07 by Carlos García Meixide, Meixide, Carlos García, David Rı́os Insua +1
Decision Sciences · #FOS: Computer and information sciences #Methodology (stat.ME) #Risk and Portfolio Optimization

paper · pdf · doi:10.48550/arxiv.2507.05170

openalex publication_date 2025/07/07 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28

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.

Citations

• Bayesian Invariance Modeling of Multi-Environment Data
• Debiased Ill-Posed Regression
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• On the half-Cauchy prior for a global scale parameter
• Generating random correlation matrices based on vines and extended onion method
• Robust Convex Optimization

Related

• Focused Bayesian Prediction
• Predictive variational inference: Learn the predictively optimal posterior distribution
• Accounting for Unobserved Confounding in Domain Generalization
• Unsupervised domain adaptation under hidden confounding
• Predictively Oriented Posteriors