Bayesian Causal Discovery Fails Under Latent Confounding.

Bayesian causal discovery is a popular method for inferring causal relationships and quantifying uncertainty in directed acyclic graphs (DAGs). However, its reliability when unobserved variables (latent confounders) influence multiple observed variables has been poorly understood. Existing work often acknowledges that confounding breaks identifiability but doesn't detail the specific ways the posterior distribution over DAGs is affected. This study focuses on linear Gaussian causal models with additive latent confounding between exactly two observed variables. Researchers derived a critical correlation threshold: if the correlation between confounded variables exceeds this threshold, the scoring function used in causal discovery will incorrectly favor graphs that include a spurious edge between these variables. Importantly, this threshold decreases as the sample size increases, meaning more data can make the model *more* prone to inferring false causal links. Beyond this threshold, the paper characterizes two distinct failure regimes for the posterior distribution, determined by the local graph structure around the confounded variables. These theoretical findings are supported by exact posterior computations on various graph structures, confirming the predicted failure behaviors.