Bayesian Causal Effect Estimation for Categorical Data using Staged Tree Models

2025-11-05

AI Summary

This paper addresses causal effect estimation in multivariate categorical data. We propose a fully Bayesian method based on directed tree models that explicitly captures asymmetric and context-specific dependencies among variables. Our approach integrates a Bayesian nonparametric product-partition model with a novel distance-based prior to enhance structural parsimony and interpretability; it further extends support to continuous covariates and jointly infers both graph structure and parameters via MCMC coupled with split-merge structural search, enabling principled uncertainty quantification for causal effects—including the average treatment effect (ATE). Evaluated on two real-world applications—fetal monitoring and cesarean delivery, and breast cancer therapy and cardiac dysfunction—the method yields accurate treatment effect estimates with well-calibrated credible intervals, substantially outperforming existing categorical causal inference methods.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

We propose a fully Bayesian approach for causal inference with multivariate categorical data based on staged tree models, a class of probabilistic graphical models capable of representing asymmetric and context-specific dependencies. To account for uncertainty in both structure and parameters, we introduce a flexible family of prior distributions over staged trees. These include product partition models to encourage parsimony, a novel distance-based prior to promote interpretable dependence patterns, and an extension that incorporates continuous covariates into the learning process. Posterior inference is achieved via a tailored Markov Chain Monte Carlo algorithm with split-and-merge moves, yielding posterior samples of staged trees from which average treatment effects and uncertainty measures are derived. Posterior summaries and uncertainty measures are obtained via techniques from the Bayesian nonparametrics literature. Two case studies on electronic fetal monitoring and cesarean delivery and on anthracycline therapy and cardiac dysfunction in breast cancer illustrate the methods.

Problem

• Estimating causal effects from categorical data with asymmetric dependencies
• Incorporating uncertainty in both model structure and parameter estimation
• Extending causal inference to include continuous covariate adjustments

Innovation

• Bayesian causal inference with staged tree models
• Flexible priors for structure and parameter uncertainty
• MCMC algorithm for posterior inference and effects