# Bayesian Network Structure Discovery Using Large Language Models

arXiv: https://arxiv.org/abs/2511.00574 · HTML: https://mlsanity.com/paper/2511.00574/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 39 references that are in the map.
- First posted on arXiv 1 Nov 2025.

## Builds on (most cited first, 23 of 23)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Causal Reasoning and Large Language Models: Opening a New Frontier for Causality](https://mlsanity.com/paper/2305.00050/) (2023)
- [Can large language models build causal graphs?](https://mlsanity.com/paper/2303.05279/) (2023)
- [Causal Discovery with Language Models as Imperfect Experts](https://mlsanity.com/paper/2307.02390/) (2023)
- [LMPriors: Pre-Trained Language Models as Task-Specific Priors](https://mlsanity.com/paper/2210.12530/) (2022)
- [Integrating Large Language Model for Improved Causal Discovery](https://mlsanity.com/paper/2306.16902/) (2023)
- [Efficient Causal Graph Discovery Using Large Language Models](https://mlsanity.com/paper/2402.01207/) (2024)
- [The impact of prior knowledge on causal structure learning](https://mlsanity.com/paper/2102.00473/) (2021)
- [ALCM: Autonomous LLM-Augmented Causal Discovery Framework](https://mlsanity.com/paper/2405.01744/) (2024)
- [pgmpy: A Python Toolkit for Bayesian Networks](https://mlsanity.com/paper/2304.08639/) (2023)
- [Causal Structure Learning Supervised by Large Language Model](https://mlsanity.com/paper/2311.11689/) (2023)
- [Meta Prompting for AI Systems](https://mlsanity.com/paper/2311.11482/) (2023)
- [Large Language Models for Constrained-Based Causal Discovery](https://mlsanity.com/paper/2406.07378/) (2024)
- [Extracting Probabilistic Knowledge from Large Language Models for Bayesian Network Parameterization](https://mlsanity.com/paper/2505.15918/) (2025)
- [bnRep: A repository of Bayesian networks from the academic literature](https://mlsanity.com/paper/2409.19158/) (2024)
- [Teaching Probabilistic Logical Reasoning to Transformers](https://mlsanity.com/paper/2305.13179/) (2023)
- [Improving Bayesian Network Structure Learning in the Presence of Measurement Error](https://mlsanity.com/paper/2011.09776/) (2020)
- [Can LLMs Leverage Observational Data? Towards Data-Driven Causal Discovery with LLMs](https://mlsanity.com/paper/2504.10936/) (2025)
- [PenPC: A Two-step Approach to Estimate the Skeletons of High Dimensional Directed Acyclic Graphs](https://mlsanity.com/paper/1405.1603/) (2014)
- [Scalability of Bayesian Network Structure Elicitation with Large Language Models: a Novel Methodology and Comparative Analysis](https://mlsanity.com/paper/2407.09311/) (2024)
- [Empirical Bayesian Approaches for Robust Constraint-based Causal Discovery under Insufficient Data](https://mlsanity.com/paper/2206.08448/) (2022)

## Built on by (most cited first, 5 of 5)

- [Grading the Unspoken: Evaluating Tacit Reasoning in Quantum Field Theory and String Theory with LLMs](https://mlsanity.com/paper/2604.14188/) (2026)
- [KG-SoftMAP: Soft Knowledge-Graph Priors for Bayesian Network Structure Learning from Sparse Discrete Data](https://mlsanity.com/paper/2606.10358/) (2026)
- [LEBGen: An LLM-Enhanced Bayesian Network Framework for Few-Shot Travel Survey Data Generation](https://mlsanity.com/paper/2609.08288/) (2026)
- [CausalArena: Benchmarking Causal Discovery in the Foundation Model Era](https://mlsanity.com/paper/2609.11897/) (2026)
- [PRISM-BN: A Controlled Corpus and Benchmark for Text-to-Parameterized Bayesian Network Extraction](https://mlsanity.com/paper/2609.21673/) (2026)

## Abstract (arXiv)

Understanding probabilistic dependencies among variables is central to analyzing complex systems. Traditional structure learning methods often require extensive observational data or are limited by manual, error-prone incorporation of expert knowledge. Recent studies have explored using large language models (LLMs) for structure learning, but most treat LLMs as auxiliary tools for pre-processing or post-processing, leaving the core learning process data-driven. In this work, we introduce a unified framework for Bayesian network structure discovery that places LLMs at the center, supporting both data-free and data-aware settings. In the data-free regime, we introduce PromptBN, which leverages LLM reasoning over variable metadata to generate a complete directed acyclic graph (DAG) in a single call. PromptBN effectively enforces global consistency and acyclicity through dual validation, achieving constant O(1) query complexity. When observational data are available, we introduce ReActBN to further refine the initial graph. ReActBN combines statistical evidence with LLM by integrating a novel ReAct-style reasoning with configurable structure scores (e.g., Bayesian Information Criterion). Experiments demonstrate that our method outperforms prior data-only, LLM-only, and hybrid baselines, particularly in low- or no-data regimes and on out-of-distribution datasets. Code is available at https://github.com/sherryzyh/llmbn.