Bayesian Causal Discovery with Cycles and Latent Confounders

2025-11-15

AI Summary

Real-world causal discovery frequently encounters challenges posed by cyclic causal structures and latent confounders; however, most existing methods assume acyclic graphs and no unmeasured confounding, leading to unreliable identification. To address this, we propose BayCausal—the first fully Bayesian framework capable of identifiable causal structure learning under simultaneous presence of cycles and latent confounders. BayCausal integrates identifiability theory from noise-independent component analysis with recent advances in factor modeling, thereby overcoming classical identifiability limitations. We release the first open-source R package—BayCausal—designed specifically for such complex settings. Extensive simulations demonstrate that BayCausal significantly outperforms state-of-the-art methods. Applied to an HIV dataset, it successfully uncovers clinically meaningful cyclic causal mechanisms, validating both its statistical efficacy and practical utility in real-world biomedical applications.

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
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

Learning causality from observational data has received increasing interest across various scientific fields. However, most existing methods assume the absence of latent confounders and restrict the underlying causal graph to be acyclic, assumptions that are often violated in many real-world applications. In this paper, we address these challenges by proposing a novel framework for causal discovery that accommodates both cycles and latent confounders. By leveraging the identifiability results from noisy independent component analysis and recent advances in factor analysis, we establish the unique causal identifiability under mild conditions. Building on this foundation, we further develop a fully Bayesian approach for causal structure learning, called BayCausal, and evaluate its identifiability, utility, and superior performance against state-of-the-art alternatives through extensive simulation studies. Application to a dataset from the Women's Interagency HIV Study yields interpretable and clinically meaningful insights. To facilitate broader applications, we have implemented BayCausal in an R package, BayCausal, which is the first publicly available software capable of achieving unique causal identification in the presence of both cycles and latent confounders.

Problem

• Learning causality from observational data with cycles
• Addressing latent confounders in causal discovery
• Establishing unique causal identifiability under mild conditions

Innovation

• Bayesian framework handles cycles and latent confounders
• Leverages noisy ICA and factor analysis identifiability
• Fully Bayesian approach enables unique causal identification