# Mitigating Prior Errors in Causal Structure Learning: A Resilient Approach via Bayesian Networks

arXiv: https://arxiv.org/abs/2306.07032 · HTML: https://mlsanity.com/paper/2306.07032/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 63 references that are in the map.
- First posted on arXiv 12 Jun 2023.

## Builds on (most cited first, 18 of 18)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Causal Reasoning and Large Language Models: Opening a New Frontier for Causality](https://mlsanity.com/paper/2305.00050/) (2023)
- [DAG-GNN: DAG Structure Learning with Graph Neural Networks](https://mlsanity.com/paper/1904.10098/) (2019)
- [A Survey on Neural Network Interpretability](https://mlsanity.com/paper/2012.14261/) (2020)
- [Gradient-Based Neural DAG Learning](https://mlsanity.com/paper/1906.02226/) (2019)
- [D'ya like DAGs? A Survey on Structure Learning and Causal Discovery](https://mlsanity.com/paper/2103.02582/) (2021)
- [On the Role of Sparsity and DAG Constraints for Learning Linear DAGs](https://mlsanity.com/paper/2006.10201/) (2020)
- [A survey of Bayesian Network structure learning](https://mlsanity.com/paper/2109.11415/) (2021)
- [Can large language models build causal graphs?](https://mlsanity.com/paper/2303.05279/) (2023)
- [Deconfounded Image Captioning: A Causal Retrospect](https://mlsanity.com/paper/2003.03923/) (2020)
- [A Graph Autoencoder Approach to Causal Structure Learning](https://mlsanity.com/paper/1911.07420/) (2019)
- [The impact of prior knowledge on causal structure learning](https://mlsanity.com/paper/2102.00473/) (2021)
- [Optimizing regularized Cholesky score for order-based learning of Bayesian networks](https://mlsanity.com/paper/1904.12360/) (2019)
- [Multiple Quantitative Trait Analysis Using Bayesian Networks](https://mlsanity.com/paper/1402.2905/) (2014)
- [Scoring and Searching over Bayesian Networks with Causal and Associative Priors](https://mlsanity.com/paper/1408.2057/) (2014)
- [A Theoretical Analysis of the BDeu Scores in Bayesian Network Structure Learning](https://mlsanity.com/paper/1607.04427/) (2016)
- [A Bayesian Approach to Recurrence in Neural Networks](https://mlsanity.com/paper/1910.11247/) (2019)
- [Learning Discriminative Bayesian Networks from High-dimensional Continuous Neuroimaging Data](https://mlsanity.com/paper/1506.06868/) (2015)

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

- [Robust Causal Discovery under Imperfect Structural Constraints](https://mlsanity.com/paper/2511.06790/) (2025)
- [CARE: Turning LLMs Into Causal Reasoning Expert](https://mlsanity.com/paper/2511.16016/) (2025)
- [Leveraging Large Language Models for Causal Discovery: a Constraint-based, Argumentation-driven Approach](https://mlsanity.com/paper/2602.16481/) (2026)
- [CausalSteward: An Agentic Divide-Conquer-Combine Copilot for Causal Discovery](https://mlsanity.com/paper/2607.01936/) (2026)
- [Integrating Background Knowledge for Scalable Causal Discovery](https://mlsanity.com/paper/2607.10456/) (2026)

## Abstract (arXiv)

Causal structure learning (CSL), a prominent technique for encoding cause-and-effect relationships among variables, through Bayesian Networks (BNs). Although recovering causal structure solely from data is a challenge, the integration of prior knowledge, revealing partial structural truth, can markedly enhance learning quality. However, current methods based on prior knowledge exhibit limited resilience to errors in the prior, with hard constraint methods disregarding priors entirely, and soft constraints accepting priors based on a predetermined confidence level, which may require expert intervention. To address this issue, we propose a strategy resilient to edge-level prior errors for CSL, thereby minimizing human intervention. We classify prior errors into different types and provide their theoretical impact on the Structural Hamming Distance (SHD) under the presumption of sufficient data. Intriguingly, we discover and prove that the strong hazard of prior errors is associated with a unique acyclic closed structure, defined as ``quasi-circle''. Leveraging this insight, a post-hoc strategy is employed to identify the prior errors by its impact on the increment of ``quasi-circles''. Through empirical evaluation on both real and synthetic datasets, we demonstrate our strategy's robustness against prior errors. Specifically, we highlight its substantial ability to resist order-reversed errors while maintaining the majority of correct prior.