# A Bayesian Approach to Learning Causal Networks

arXiv: https://arxiv.org/abs/1302.4958 · HTML: https://mlsanity.com/paper/1302.4958/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Feb 2013.

## Built on by (most cited first, 20 of 20)

- [Causal Inference for Time series Analysis: Problems, Methods and Evaluation](https://mlsanity.com/paper/2102.05829/) (2021)
- [Active Bayesian Causal Inference](https://mlsanity.com/paper/2206.02063/) (2022)
- [Self-Compatibility: Evaluating Causal Discovery without Ground Truth](https://mlsanity.com/paper/2307.09552/) (2023)
- [Causal Structure Learning Supervised by Large Language Model](https://mlsanity.com/paper/2311.11689/) (2023)
- [Estimating Interventional Distributions with Uncertain Causal Graphs through Meta-Learning](https://mlsanity.com/paper/2507.05526/) (2025)
- [Bivariate Causal Discovery using Bayesian Model Selection](https://mlsanity.com/paper/2306.02931/) (2023)
- [Active causal structure learning with advice](https://mlsanity.com/paper/2305.19588/) (2023)
- [Quantitative probing: Validating causal models using quantitative domain knowledge](https://mlsanity.com/paper/2209.03013/) (2022)
- [Effective Bayesian Causal Inference via Structural Marginalisation and Autoregressive Orders](https://mlsanity.com/paper/2402.14781/) (2024)
- [Continuous Bayesian Model Selection for Multivariate Causal Discovery](https://mlsanity.com/paper/2411.10154/) (2024)
- [Causality from Bottom to Top: A Survey](https://mlsanity.com/paper/2403.11219/) (2024)
- [The interventional Bayesian Gaussian equivalent score for Bayesian causal inference with unknown soft interventions](https://mlsanity.com/paper/2205.02602/) (2022)
- [Causal Discovery under Off-Target Interventions](https://mlsanity.com/paper/2402.08229/) (2024)
- [Business analytics meets artificial intelligence: Assessing the demand effects of discounts on Swiss train tickets](https://mlsanity.com/paper/2105.01426/) (2021)
- [Enhancing the Performance of Neural Networks Through Causal Discovery and Integration of Domain Knowledge](https://mlsanity.com/paper/2311.17303/) (2023)
- [Boosting Efficiency in Task-Agnostic Exploration through Causal Knowledge](https://mlsanity.com/paper/2407.20506/) (2024)
- [Quotient Normalized Maximum Likelihood Criterion for Learning Bayesian Network Structures](https://mlsanity.com/paper/2408.14935/) (2024)
- [Likelihoods and Parameter Priors for Bayesian Networks](https://mlsanity.com/paper/2105.06241/) (2021)
- [Causality and Interpretability for Electrical Distribution System faults](https://mlsanity.com/paper/2508.02524/) (2025)
- [Planning under Distribution Shifts with Causal POMDPs](https://mlsanity.com/paper/2602.23545/) (2026)

## Abstract (arXiv)

Whereas acausal Bayesian networks represent probabilistic independence, causal Bayesian networks represent causal relationships. In this paper, we examine Bayesian methods for learning both types of networks. Bayesian methods for learning acausal networks are fairly well developed. These methods often employ assumptions to facilitate the construction of priors, including the assumptions of parameter independence, parameter modularity, and likelihood equivalence. We show that although these assumptions also can be appropriate for learning causal networks, we need additional assumptions in order to learn causal networks. We introduce two sufficient assumptions, called {em mechanism independence} and {em component independence}. We show that these new assumptions, when combined with parameter independence, parameter modularity, and likelihood equivalence, allow us to apply methods for learning acausal networks to learn causal networks.