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# Bayesian federated estimation of causal effects from observational data

*Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence*, PMLR 180:2024-2034, 2022.

#### Abstract

We propose a Bayesian framework for estimating causal effects from federated observational data sources. Bayesian causal inference is an important approach to learning the distribution of the causal estimands and understanding the uncertainty of causal effects. Our framework estimates the posterior distributions of the causal effects to compute the higher-order statistics that capture the uncertainty. We integrate local causal effects from different data sources without centralizing them. We then estimate the treatment effects from observational data using a non-parametric reformulation of the classical potential outcomes framework. We model the potential outcomes as a random function distributed by Gaussian processes, with defining parameters that can be efficiently learned from multiple data sources. Our method avoids exchanging raw data among the sources, thus contributing towards privacy-preserving causal learning. The promise of our approach is demonstrated through a set of simulated and real-world examples.