Bayesian Causal Discovery with Cycles and Latent Confounders

TL;DR

This paper introduces BayCausal, a Bayesian framework for causal discovery that uniquely identifies causal structures in data with cycles and latent confounders, supported by theoretical guarantees and practical software implementation.

Contribution

It presents the first Bayesian method capable of causal discovery with cycles and latent confounders, backed by identifiability results and an R package implementation.

Findings

BayCausal outperforms existing methods in simulations.

Application yields meaningful clinical insights.

Software is publicly available for broader use.

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.