# Coupling Noisy Pairwise Knowledge to the DAG Posterior for Causal Discovery

arXiv: https://arxiv.org/abs/2610.04559 · HTML: https://mlsanity.com/paper/2610.04559/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 35 references that are in the map.
- First posted on arXiv 3 Oct 2026.

## Builds on (most cited first, 19 of 19)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm](https://mlsanity.com/paper/1608.04471/) (2016)
- [Causal Reasoning and Large Language Models: Opening a New Frontier for Causality](https://mlsanity.com/paper/2305.00050/) (2023)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [Causal Parrots: Large Language Models May Talk Causality But Are Not Causal](https://mlsanity.com/paper/2308.13067/) (2023)
- [DiBS: Differentiable Bayesian Structure Learning](https://mlsanity.com/paper/2105.11839/) (2021)
- [A survey of Bayesian Network structure learning](https://mlsanity.com/paper/2109.11415/) (2021)
- [Causal Discovery with Language Models as Imperfect Experts](https://mlsanity.com/paper/2307.02390/) (2023)
- [Efficient Causal Graph Discovery Using Large Language Models](https://mlsanity.com/paper/2402.01207/) (2024)
- [Causal Order: The Key to Leveraging Imperfect Experts in Causal Inference](https://mlsanity.com/paper/2310.15117/) (2023)
- [Parameter Priors for Directed Acyclic Graphical Models and the Characterization of Several Probability Distributions](https://mlsanity.com/paper/1301.6697/) (2013)
- [Addendum on the scoring of Gaussian directed acyclic graphical models](https://mlsanity.com/paper/1402.6863/) (2014)
- [Data Analysis with Bayesian Networks: A Bootstrap Approach](https://mlsanity.com/paper/1301.6695/) (2013)
- [Large Language Models are Effective Priors for Causal Graph Discovery](https://mlsanity.com/paper/2405.13551/) (2024)
- [Learning Bayesian Networks in the Presence of Structural Side Information](https://mlsanity.com/paper/2112.10884/) (2021)
- [Incorporating Expert Knowledge into Bayesian Causal Discovery of Mixtures of Directed Acyclic Graphs](https://mlsanity.com/paper/2510.06735/) (2025)
- [Improving constraint-based discovery with robust propagation and reliable LLM priors](https://mlsanity.com/paper/2509.23570/) (2025)
- [KG-SoftMAP: Soft Knowledge-Graph Priors for Bayesian Network Structure Learning from Sparse Discrete Data](https://mlsanity.com/paper/2606.10358/) (2026)

## 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.