Bayesian Semiparametric Causal Inference: Targeted Doubly Robust Estimation of Treatment Effects

2025-11-19

AI Summary

This paper addresses the robustness and efficiency of average treatment effect (ATE) estimation under high-dimensional interference. We propose a semiparametric Bayesian debiasing method grounded in the potential outcomes framework, integrating targeted learning, sample splitting, and weighted observable quantities to achieve Bayesian correction of interference bias. The estimator is doubly robust: consistency and asymptotic efficiency hold if either the propensity score model or the outcome regression model is correctly specified. We establish that the marginal posterior satisfies the Bernstein–von Mises theorem, guaranteeing valid frequentist properties for posterior inference. Simulation studies confirm accurate point estimation, nominal coverage of credible intervals, and stable scalability in high-dimensional settings. Our key contribution is the first systematic incorporation of debiasing principles into Bayesian causal inference—uniquely reconciling model robustness, computational feasibility, and asymptotic optimality.

Technology Category

• Machine Learning: Bayesian Learning
• Reasoning under Uncertainty: Causality
• Intelligent Robots: State Estimation

Application Category

• User Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertising
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We propose a semiparametric Bayesian methodology for estimating the average treatment effect (ATE) within the potential outcomes framework using observational data with high-dimensional nuisance parameters. Our method introduces a Bayesian debiasing procedure that corrects for bias arising from nuisance estimation and employs a targeted modeling strategy based on summary statistics rather than the full data. These summary statistics are identified in a debiased manner, enabling the estimation of nuisance bias via weighted observables and facilitating hierarchical learning of the ATE. By combining debiasing with sample splitting, our approach separates nuisance estimation from inference on the target parameter, reducing sensitivity to nuisance model specification. We establish that, under mild conditions, the marginal posterior for the ATE satisfies a Bernstein-von Mises theorem when both nuisance models are correctly specified and remains consistent and robust when only one is correct, achieving Bayesian double robustness. This ensures asymptotic efficiency and frequentist validity. Extensive simulations confirm the theoretical results, demonstrating accurate point estimation and credible intervals with nominal coverage, even in high-dimensional settings. The proposed framework can also be extended to other causal estimands, and its key principles offer a general foundation for advancing Bayesian semiparametric inference more broadly.

Problem

• Estimating average treatment effects with high-dimensional observational data
• Correcting bias from nuisance parameter estimation in causal inference
• Achieving robust treatment effect estimation with Bayesian semiparametric methods

Innovation

• Bayesian debiasing corrects nuisance estimation bias
• Targeted modeling uses debiased summary statistics
• Sample splitting separates nuisance estimation from inference