# Efficient Sampling and Structure Learning of Bayesian Networks

arXiv: https://arxiv.org/abs/1803.07859 · HTML: https://mlsanity.com/paper/1803.07859/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Mar 2018.

## Built on by (most cited first, 28 of 28)

- [Bayesian Structure Learning with Generative Flow Networks](https://mlsanity.com/paper/2202.13903/) (2022)
- [A survey of Bayesian Network structure learning](https://mlsanity.com/paper/2109.11415/) (2021)
- [Differentiable DAG Sampling](https://mlsanity.com/paper/2203.08509/) (2022)
- [Bayesian structure learning and sampling of Bayesian networks with the R package BiDAG](https://mlsanity.com/paper/2105.00488/) (2021)
- [Tractable Uncertainty for Structure Learning](https://mlsanity.com/paper/2204.14170/) (2022)
- [Benchpress: A Scalable and Versatile Workflow for Benchmarking Structure Learning Algorithms](https://mlsanity.com/paper/2107.03863/) (2021)
- [bnRep: A repository of Bayesian networks from the academic literature](https://mlsanity.com/paper/2409.19158/) (2024)
- [Better Simulations for Validating Causal Discovery with the DAG-Adaptation of the Onion Method](https://mlsanity.com/paper/2405.13100/) (2024)
- [Learning Latent Structural Causal Models](https://mlsanity.com/paper/2210.13583/) (2022)
- [The interventional Bayesian Gaussian equivalent score for Bayesian causal inference with unknown soft interventions](https://mlsanity.com/paper/2205.02602/) (2022)
- [A Bayesian Take on Gaussian Process Networks](https://mlsanity.com/paper/2306.11380/) (2023)
- [Structure Learning with Adaptive Random Neighborhood Informed MCMC](https://mlsanity.com/paper/2311.00599/) (2023)
- [Sample Efficient Bayesian Learning of Causal Graphs from Interventions](https://mlsanity.com/paper/2410.20089/) (2024)
- [Embracing Discrete Search: A Reasonable Approach to Causal Structure Learning](https://mlsanity.com/paper/2510.04970/) (2025)
- [Bayesian Causal Inference with Gaussian Process Networks](https://mlsanity.com/paper/2402.00623/) (2024)
- [The Dual PC Algorithm and the Role of Gaussianity for Structure Learning of Bayesian Networks](https://mlsanity.com/paper/2112.09036/) (2021)
- [Learning and interpreting asymmetry-labeled DAGs: a case study on COVID-19 fear](https://mlsanity.com/paper/2301.00629/) (2023)
- [BCDAG: An R package for Bayesian structure and Causal learning of Gaussian DAGs](https://mlsanity.com/paper/2201.12003/) (2022)
- [Latent Variable Models for Bayesian Causal Discovery](https://mlsanity.com/paper/2207.05723/) (2022)
- [Tuning structure learning algorithms with out-of-sample and resampling strategies](https://mlsanity.com/paper/2306.13932/) (2023)
- [Scalable Variational Causal Discovery Unconstrained by Acyclicity](https://mlsanity.com/paper/2407.04992/) (2024)
- [High-Dimensional Inference in Bayesian Networks](https://mlsanity.com/paper/2112.09217/) (2021)
- [Scalable Structure Learning for Sparse Context-Specific Systems](https://mlsanity.com/paper/2402.07762/) (2024)
- [Exact discovery is polynomial for certain sparse causal Bayesian networks](https://mlsanity.com/paper/2406.15012/) (2024)
- [Learning Dynamic Bayesian Networks from Data: Foundations, First Principles and Numerical Comparisons](https://mlsanity.com/paper/2406.17585/) (2024)
- [An Efficient Procedure for Computing Bayesian Network Structure Learning](https://mlsanity.com/paper/2407.17072/) (2024)
- [Scaling Up Bayesian DAG Sampling](https://mlsanity.com/paper/2510.25254/) (2025)
- [Causal Preference Elicitation](https://mlsanity.com/paper/2602.01483/) (2026)

## Abstract (arXiv)

Bayesian networks are probabilistic graphical models widely employed to understand dependencies in high dimensional data, and even to facilitate causal discovery. Learning the underlying network structure, which is encoded as a directed acyclic graph (DAG) is highly challenging mainly due to the vast number of possible networks in combination with the acyclicity constraint. Efforts have focussed on two fronts: constraint-based methods that perform conditional independence tests to exclude edges and score and search approaches which explore the DAG space with greedy or MCMC schemes. Here we synthesise these two fields in a novel hybrid method which reduces the complexity of MCMC approaches to that of a constraint-based method. Individual steps in the MCMC scheme only require simple table lookups so that very long chains can be efficiently obtained. Furthermore, the scheme includes an iterative procedure to correct for errors from the conditional independence tests. The algorithm offers markedly superior performance to alternatives, particularly because DAGs can also be sampled from the posterior distribution, enabling full Bayesian model averaging for much larger Bayesian networks.