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Explainable Federated Bayesian Causal Inference and Its Application in Advanced Manufacturing

Xiaofeng Xiao, Khawlah Alharbi, Pengyu Zhang, Hantang Qin, Xubo Yue

TL;DR

This work addresses the need for privacy-preserving causal inference in distributed manufacturing by introducing xFBCI, a federated Bayesian framework that learns personalized posteriors via Expectation Propagation and then estimates causal effects with propensity score matching. By treating the propensity score as $e(x)=Pr(W=1|x)$ and matching on these scores, xFBCI isolates treatment effects across heterogeneous clients without sharing raw data. The approach is validated on simulated homogeneous, heterogeneous, and complex heterogeneous settings, and demonstrated on real Electrohydrodynamic (EHD) printing data, where it outperforms baseline federated methods in parameter recovery and ATE estimation while maintaining privacy. The results indicate strong robustness to distributional shifts, data imbalance, and high dimensionality, with practical implications for optimizing manufacturing processes through explainable causal insights.

Abstract

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.

Explainable Federated Bayesian Causal Inference and Its Application in Advanced Manufacturing

TL;DR

This work addresses the need for privacy-preserving causal inference in distributed manufacturing by introducing xFBCI, a federated Bayesian framework that learns personalized posteriors via Expectation Propagation and then estimates causal effects with propensity score matching. By treating the propensity score as and matching on these scores, xFBCI isolates treatment effects across heterogeneous clients without sharing raw data. The approach is validated on simulated homogeneous, heterogeneous, and complex heterogeneous settings, and demonstrated on real Electrohydrodynamic (EHD) printing data, where it outperforms baseline federated methods in parameter recovery and ATE estimation while maintaining privacy. The results indicate strong robustness to distributional shifts, data imbalance, and high dimensionality, with practical implications for optimizing manufacturing processes through explainable causal insights.

Abstract

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.
Paper Structure (33 sections, 24 equations, 5 figures, 15 tables, 1 algorithm)

This paper contains 33 sections, 24 equations, 5 figures, 15 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Motivation
  3. Contributions
  4. Literature Review
  5. Bayesian Federated Learning.
  6. Bayesian Causal Inference.
  7. Causal Inference in Manufacturing.
  8. Method
  9. Notations
  10. Federated Bayesian Variational Inference
  11. Treatment Effect
  12. Simulation
  13. One Simple Homogeneous Case
  14. Case 1.
  15. Evaluation Metrics.
  16. ...and 18 more sections

Figures (5)

  • Figure 1: Schematic of EHD printing setup.
  • Figure 2: Boxplot of the results from 10 replications in Case 1. In (b), the green line indicates the mean value of the true ATE across 10 replications.
  • Figure 3: Box-plot of results in Case 6.
  • Figure 4: Examples of EHD printed lines.
  • Figure 5: Bar-plot of the MSE results for before implementing matching (Before), after implementing matching of xFBCI, Ditto, and Individual for two clients. We utilize Client 1 and Client 2 here for representing the two EHD datasets.