mlsanityData to 14 Oct 2026

Coupling Noisy Pairwise Knowledge to the DAG Posterior for Causal Discovery

arXiv 2610.04559 ↗First posted 3 Oct 2026cs.LG cs.AI stat.MLcited by 0

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Abstract (arXiv)

External causal reports can improve structure learning from limited observations, but their reliability varies across sources and variable pairs. We introduce HB-NoisyKG, a Bayesian framework that combines observational data with repeated causal reports from sources such as large language models. Each report is a noisy observation of a direct pair state implied by one DAG. A feature-conditioned Beta prior pools information about pair reliability, and a shared error matrix captures systematic mistakes. Alternating inference uses the graph posterior to refine reliability estimates, which determine how reports influence subsequent graph updates. The report likelihood uses only graph pair-state marginals, so the same observation layer supports discrete and continuous likelihoods in graph-only and joint inference. Against an 80-restart no-KG baseline, HB uses at most 80 total restarts and lowers mean SHD from 22.39 to 16.06 on five discrete benchmarks. On a physical light tunnel with random variable IDs and retained descriptions, HB lowers SHD from 39.00 for no-KG to 27.30. On continuous Sachs, graph-only BGe raises AUROC by 0.121 over no-KG Top-K. In a controlled synthetic study, continued updating also reduces mean reliability estimation error and held-out report log loss compared with one-time estimation.

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References · 19

  1. 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 752
  2. 2016Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithmcited by 507
  3. 2023Causal Reasoning and Large Language Models: Opening a New Frontier for Causalitycited by 353
  4. 2020On the Role of Sparsity and DAG Constraints for Learning Linear DAGscited by 191
  5. 2013Learning Bayesian Networks: The Combination of Knowledge and Statistical Datacited by 187
  6. 2023Causal Parrots: Large Language Models May Talk Causality But Are Not Causalcited by 150
  7. 2021DiBS: Differentiable Bayesian Structure Learningcited by 106
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  9. 2023Causal Discovery with Language Models as Imperfect Expertscited by 64
  10. 2024Efficient Causal Graph Discovery Using Large Language Modelscited by 53
  11. 2023Causal Order: The Key to Leveraging Imperfect Experts in Causal Inferencecited by 48
  12. 2013Parameter Priors for Directed Acyclic Graphical Models and the Characterization of Several Probability Distributionscited by 42
7 more
  1. 2014Addendum on the scoring of Gaussian directed acyclic graphical modelscited by 33
  2. 2013Data Analysis with Bayesian Networks: A Bootstrap Approachcited by 32
  3. 2024Large Language Models are Effective Priors for Causal Graph Discoverycited by 24
  4. 2021Learning Bayesian Networks in the Presence of Structural Side Informationcited by 12
  5. 2025Incorporating Expert Knowledge into Bayesian Causal Discovery of Mixtures of Directed Acyclic Graphscited by 2
  6. 2025Improving constraint-based discovery with robust propagation and reliable LLM priorscited by 1
  7. 2026KG-SoftMAP: Soft Knowledge-Graph Priors for Bayesian Network Structure Learning from Sparse Discrete Datacited by 1

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