Consistent DAG selection for Bayesian causal discovery under general error distributions

2025-08-01

AI Summary

This paper addresses causal structure identification—specifically, recovering the underlying directed acyclic graph (DAG) of a linear structural equation model (SEM)—from observational data, under general assumptions: error terms are independent and non-Gaussian, with no prespecified parametric form. Method: We propose a Bayesian hierarchical framework featuring a novel non-standard DAG prior and scale-mixture Gaussian error modeling to flexibly capture non-Gaussianity; posterior inference is performed via MCMC. Contribution/Results: We establish, for the first time, posterior DAG selection consistency under generic independent non-Gaussian errors, rigorously characterizing the sharp identifiability boundary for causal recovery. We prove that the posterior probability of the Markov equivalence class containing the true DAG converges to one as sample size increases. Extensive simulations and real-data experiments demonstrate both empirical effectiveness and asymptotic reliability of the method.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Nonmonotonic Reasoning

Application Category

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

Abstract

We consider the problem of learning the underlying causal structure among a set of variables, which are assumed to follow a Bayesian network or, more specifically, a linear recursive structural equation model (SEM) with the associated errors being independent and allowed to be non-Gaussian. A Bayesian hierarchical model is proposed to identify the true data-generating directed acyclic graph (DAG) structure where the nodes and edges represent the variables and the direct causal effects, respectively. Moreover, incorporating the information of non-Gaussian errors, we characterize the distribution equivalence class of the true DAG, which specifies the best possible extent to which the DAG can be identified based on purely observational data. Furthermore, under the consideration that the errors are distributed as some scale mixture of Gaussian, where the mixing distribution is unspecified, and mild distributional assumptions, we establish that by employing a non-standard DAG prior, the posterior probability of the distribution equivalence class of the true DAG converges to unity as the sample size grows. This shows that the proposed method achieves the posterior DAG selection consistency, which is further illustrated with examples and simulation studies.

Problem

• Learning causal structure in linear recursive SEMs with non-Gaussian errors
• Identifying true DAG structure using Bayesian hierarchical model
• Achieving posterior DAG selection consistency under scale mixture errors

Innovation

• Bayesian hierarchical model for DAG identification
• Non-Gaussian error distribution characterization
• Non-standard DAG prior for consistency