How Does Bayesian Causal Discovery Fail? Characterising Structural Consequences in Linear Gaussian Networks under Latent Confounding
The study analyzes Bayesian causal discovery failures in linear Gaussian networks specifically under additive latent confounding between two observed variables. A critical correlation threshold is derived, above which the scoring function incorrectly favors a spurious edge between confounded variables. This threshold decreases as sample size increases, meaning larger datasets actually lower the correlation required to induce this specific error. Two distinct posterior failure regimes are charact
Analysis
TL;DR
- The study analyzes Bayesian causal discovery failures in linear Gaussian networks specifically under additive latent confounding between two observed variables.
- A critical correlation threshold is derived, above which the scoring function incorrectly favors a spurious edge between confounded variables.
- This threshold decreases as sample size increases, meaning larger datasets actually lower the correlation required to induce this specific error.
- Two distinct posterior failure regimes are characterized based on the local graph structure surrounding the confounded variables.
- Exact posterior computations on various graph structures validate the existence of these predicted failure regimes.
Why It Matters
This research provides a rigorous mathematical characterization of how latent confounding distorts Bayesian causal inference, moving beyond simple identifiability claims to specific posterior behaviors. For practitioners, it highlights a counterintuitive risk where increasing data volume can exacerbate certain types of structural errors in the presence of unobserved confounders. Understanding these failure modes is crucial for developing robust causal discovery algorithms and interpreting results in observational studies where latent variables are likely present.
Technical Details
- Model Assumptions: The analysis focuses on linear Gaussian causal models with additive latent confounding affecting exactly two observed variables.
- Threshold Derivation: The authors mathematically derive a critical correlation threshold that determines when the score function prefers a spurious direct edge between confounded nodes over the true latent structure.
- Sample Size Dependency: It is proven that the critical correlation threshold is inversely related to sample size; higher N reduces the correlation needed to trigger the spurious edge preference.
- Failure Regimes: Beyond the threshold, the posterior distribution splits into two distinct failure regimes, dependent on the local topological structure around the confounded pair.
- Validation Method: Findings are supported by exact posterior computations performed on multiple graph structures to empirically demonstrate the theoretical failure regimes.
Industry Insight
- Data Quantity vs. Quality: Practitioners should be aware that simply collecting more data does not guarantee better causal recovery in the presence of latent confounding; it may actually solidify incorrect structural beliefs if correlations exceed the derived threshold.
- Diagnostic Metrics: Monitoring the correlation strength between variable pairs can serve as an early warning signal for potential spurious edge formation in Bayesian causal discovery pipelines.
- Algorithm Development: Future causal discovery methods should incorporate explicit penalties or mechanisms to detect and correct for latent confounding effects, particularly in high-sample-size regimes where standard scores might mislead.
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