# The impact of prior knowledge on causal structure learning

arXiv: https://arxiv.org/abs/2102.00473 · HTML: https://mlsanity.com/paper/2102.00473/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 61 references that are in the map.
- First posted on arXiv 31 Jan 2021.

## Builds on (most cited first, 9 of 9)

- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [Large-scale empirical validation of Bayesian Network structure learning algorithms with noisy data](https://mlsanity.com/paper/2005.09020/) (2020)
- [Learning Bayesian Networks: A Unification for Discrete and Gaussian Domains](https://mlsanity.com/paper/1302.4957/) (2013)
- [Properties of Bayesian Belief Network Learning Algorithms](https://mlsanity.com/paper/1302.6792/) (2013)
- [Formalizing Neurath's Ship: Approximate Algorithms for Online Causal Learning](https://mlsanity.com/paper/1609.04212/) (2016)
- [An Empirical-Bayes Score for Discrete Bayesian Networks](https://mlsanity.com/paper/1605.03884/) (2016)
- [Learning Bayesian Networks that enable full propagation of evidence](https://mlsanity.com/paper/2004.04571/) (2020)
- [Learning Bayesian networks from demographic and health survey data](https://mlsanity.com/paper/1912.00715/) (2019)
- [Improving Bayesian Network Structure Learning in the Presence of Measurement Error](https://mlsanity.com/paper/2011.09776/) (2020)

## Built on by (most cited first, 30 of 35)

- [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)
- [Integrating Large Language Model for Improved Causal Discovery](https://mlsanity.com/paper/2306.16902/) (2023)
- [Causal Order: The Key to Leveraging Imperfect Experts in Causal Inference](https://mlsanity.com/paper/2310.15117/) (2023)
- [ALCM: Autonomous LLM-Augmented Causal Discovery Framework](https://mlsanity.com/paper/2405.01744/) (2024)
- [Causal Structure Learning Supervised by Large Language Model](https://mlsanity.com/paper/2311.11689/) (2023)
- [Large Language Models for Constrained-Based Causal Discovery](https://mlsanity.com/paper/2406.07378/) (2024)
- [CausalGraph2LLM: Evaluating LLMs for Causal Queries](https://mlsanity.com/paper/2410.15939/) (2024)
- [bnRep: A repository of Bayesian networks from the academic literature](https://mlsanity.com/paper/2409.19158/) (2024)
- [Causal Discovery and Knowledge Injection for Contestable Neural Networks (with Appendices)](https://mlsanity.com/paper/2205.09787/) (2022)
- [Mitigating Prior Errors in Causal Structure Learning: A Resilient Approach via Bayesian Networks](https://mlsanity.com/paper/2306.07032/) (2023)
- [Causal discovery using dynamically requested knowledge](https://mlsanity.com/paper/2310.11154/) (2023)
- [Bayesian Network Structure Discovery Using Large Language Models](https://mlsanity.com/paper/2511.00574/) (2025)
- [Domain Knowledge in A*-Based Causal Discovery](https://mlsanity.com/paper/2208.08247/) (2022)
- [Causal Discovery over High-Dimensional Structured Hypothesis Spaces with Causal Graph Partitioning](https://mlsanity.com/paper/2406.06348/) (2024)
- [Using GPT-4 to guide causal machine learning](https://mlsanity.com/paper/2407.18607/) (2024)
- [EDGE: Error Dependency Graph-Guided Multi-Error Attribution in Multi-Agent LLM Systems](https://mlsanity.com/paper/2609.01360/) (2026)
- [CKH: Causal Knowledge Hierarchy for Estimating Structural Causal Models from Data and Priors](https://mlsanity.com/paper/2204.13775/) (2022)
- [Learning to Defer for Causal Discovery with Imperfect Experts](https://mlsanity.com/paper/2502.13132/) (2025)
- [Incorporating Expert Knowledge into Bayesian Causal Discovery of Mixtures of Directed Acyclic Graphs](https://mlsanity.com/paper/2510.06735/) (2025)
- [Robust Causal Discovery under Imperfect Structural Constraints](https://mlsanity.com/paper/2511.06790/) (2025)
- [Causal Discovery on Higher-Order Interactions](https://mlsanity.com/paper/2511.14206/) (2025)
- [Dynamic Expert-Guided Model Averaging for Causal Discovery](https://mlsanity.com/paper/2601.16715/) (2026)
- [Integrating Probabilistic Trees and Causal Networks for Clinical and Epidemiological Data](https://mlsanity.com/paper/2501.15973/) (2025)
- [Less Greedy Equivalence Search](https://mlsanity.com/paper/2506.22331/) (2025)
- [Shapley-PC: Constraint-based Causal Structure Learning with a Shapley Inspired Framework](https://mlsanity.com/paper/2312.11582/) (2023)
- [Sequential Causal Discovery with Noisy Language Model Priors](https://mlsanity.com/paper/2506.16234/) (2025)
- [Towards Privacy-Aware Bayesian Networks: A Credal Approach](https://mlsanity.com/paper/2509.18949/) (2025)
- [Linear Causal Discovery with Interventional Constraints](https://mlsanity.com/paper/2510.26342/) (2025)
- [Causal Discovery Should Embrace the Wisdom of the Crowd](https://mlsanity.com/paper/2603.02678/) (2026)

## Abstract (arXiv)

Causal Bayesian networks have become a powerful technology for reasoning under uncertainty in areas that require transparency and explainability, by relying on causal assumptions that enable us to simulate hypothetical interventions. The graphical structure of such models can be estimated by structure learning algorithms, domain knowledge, or a combination of both. Various knowledge approaches have been proposed in the literature that enable us to specify prior knowledge that constrains or guides these algorithms. This paper introduces some novel, and also describes some existing, knowledge-based approaches that enable us to combine structure learning with knowledge obtained from heterogeneous sources. We investigate the impact of these approaches on structure learning across different algorithms, case studies and settings that we might encounter in practice. Each approach is assessed in terms of effectiveness and efficiency, including graphical accuracy, model fitting, complexity, and runtime; making this the first paper that provides a comparative evaluation of a wide range of knowledge approaches for structure learning. Because the value of knowledge depends on what data are available, we illustrate the results both with limited and big data. While the overall results show that knowledge becomes less important with big data due to higher learning accuracy rendering knowledge less important, some of the knowledge approaches are found to be more important with big data. Amongst the main conclusions is the observation that reduced search space obtained from knowledge does not always imply reduced computational complexity, perhaps because the relationships implied by the data and knowledge are in tension.