Bayesian Causal Discovery Fails Under Latent Confounding.

Debargha Ghosh, Silja Renooij, Anna Kononova· July 13, 2026 View original

Summary

This research analyzes how Bayesian causal discovery methods fail under latent confounding in linear Gaussian models, identifying a critical correlation threshold that favors spurious edges and characterizing distinct posterior failure regimes. The findings show that more data can paradoxically lower the threshold for favoring incorrect causal links.

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.

Why it matters

Professionals relying on causal inference for decision-making must be aware of the specific ways latent confounding can lead to incorrect conclusions, especially as data volume increases, potentially misguiding strategic choices.

How to implement this in your domain

  1. 1Scrutinize causal inference models for potential latent confounders, particularly in linear Gaussian settings.
  2. 2Implement sensitivity analyses to assess the robustness of causal conclusions to unobserved variables.
  3. 3Prioritize domain expertise to identify and account for potential confounders before model deployment.
  4. 4Be cautious when interpreting strong correlations as direct causal links, especially with large datasets.
  5. 5Explore alternative causal discovery methods designed to handle latent confounding more robustly.

Who benefits

HealthcareFinanceSocial SciencesMarketingPublic Policy

Key takeaways

  • Latent confounding can cause Bayesian causal discovery to infer spurious causal links.
  • A critical correlation threshold exists, above which false edges are favored.
  • More data can paradoxically *increase* the likelihood of inferring spurious causal links under confounding.
  • Understanding local graph structure helps characterize specific failure regimes.

Original post by Debargha Ghosh, Silja Renooij, Anna Kononova

"arXiv:2607.09449v1 Announce Type: new 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, a…"

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Originally posted by Debargha Ghosh, Silja Renooij, Anna Kononova on X · view source

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