Explainable Federated Bayesian Causal Inference and Its Application in Advanced Manufacturing

Causal inference has recently gained notable attention across various fields like biology, healthcare, and environmental science, especially within explainable artificial intelligence (xAI) systems, for uncovering the causal relationships among multiple variables and outcomes. Yet, it has not been fully recognized and deployed in the manufacturing systems. In this paper, we introduce an explainable, scalable, and flexible federated Bayesian learning framework, \texttt{xFBCI}, designed to explore causality through treatment effect estimation in distributed manufacturing systems. By leveraging federated Bayesian learning, we efficiently estimate posterior of local parameters to derive the propensity score for each client without accessing local private data. These scores are then used to estimate the treatment effect using propensity score matching (PSM). Through simulations on various datasets and a real-world Electrohydrodynamic (EHD) printing data, we demonstrate that our approach outperforms standard Bayesian causal inference methods and several state-of-the-art federated learning benchmarks.