Instrumental and Proximal Causal Inference with Gaussian Processes

TL;DR

This paper introduces a Gaussian Process framework for causal inference with instrumental and proximal methods, providing reliable uncertainty quantification and systematic model selection, enhancing predictive accuracy and decision-making under unobserved confounding.

Contribution

It develops a Deconditional Gaussian Process model that unifies kernel estimators with principled uncertainty quantification and model selection for causal inference with unobserved confounders.

Findings

Strong predictive performance demonstrated

Well-calibrated epistemic uncertainty quantified

Effective model selection via marginal log-likelihood

Abstract

Instrumental variable (IV) and proximal causal learning (Proxy) methods are central frameworks for causal inference in the presence of unobserved confounding. Despite substantial methodological advances, existing approaches rarely provide reliable epistemic uncertainty (EU) quantification. We address this gap through a Deconditional Gaussian Process (DGP) framework for uncertainty-aware causal learning. Our formulation recovers popular kernel estimators as the posterior mean, ensuring predictive precision, while the posterior variance yields principled and well-calibrated EU. Moreover, the probabilistic structure enables systematic model selection via marginal log-likelihood optimization. Empirical results demonstrate strong predictive performance alongside informative EU quantification, evaluated via empirical coverage frequencies and decision-aware accuracy rejection curves. Together, our approach provides a unified, practical solution for causal inference under unobserved confounding with reliable uncertainty.