How Does Bayesian Causal Discovery Fail? Characterising Structural Consequences in Linear Gaussian Networks under Latent Confounding

2026-07-10

AI Summary

This study addresses the issue that Bayesian causal discovery methods may erroneously favor graph structures containing spurious edges in the presence of latent confounding, a phenomenon whose underlying mechanism remains poorly understood. Focusing on two-variable linear Gaussian causal models subject to additive latent confounding, this work provides the first quantitative characterization of Bayesian posterior failure: it derives a critical correlation threshold beyond which spurious edges are preferred and reveals that increasing sample size paradoxically lowers this threshold, thereby exacerbating misidentification risk. Through exact posterior computation and graphical score analysis, the authors identify two distinct modes of posterior failure dictated by local graph structure and validate their theoretical predictions across multiple graph configurations.

Abstract

Bayesian causal discovery is widely used for its ability to quantify epistemic uncertainty over directed acyclic graphs (DAGs) through posterior inference. However, its behaviour under latent confounding remains poorly understood, as existing work typically notes that confounding breaks identifiability without characterising how the posterior distribution over DAGs responds. In this work, we analyse posterior behaviour under latent confounding in linear Gaussian causal models, focusing on additive latent confounding between exactly two observed variables. We derive a critical correlation threshold above which the score function favours graphs with a spurious edge between the confounded variables, and show that this threshold decreases with sample size -- more data lowers the correlation required for the spurious edge to be favoured. Beyond this threshold, we characterize two distinct posterior failure regimes determined by the local structure around the confounded variables. Our findings are supported by exact posterior computations on multiple graph structures, demonstrating both the predicted failure regimes.

Problem

• Bayesian causal discovery
• latent confounding
• linear Gaussian networks
• posterior failure
• structural bias

Innovation

• Bayesian causal discovery
• latent confounding
• posterior failure regimes
• linear Gaussian models
• spurious edge