mlsanityData to 7 Oct 2026

A survey of Bayesian Network structure learning

arXiv 2109.11415 ↗First posted 23 Sep 2021cs.LG cs.AIcited by 85

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Abstract (arXiv)

Bayesian Networks (BNs) have become increasingly popular over the last few decades as a tool for reasoning under uncertainty in fields as diverse as medicine, biology, epidemiology, economics and the social sciences. This is especially true in real-world areas where we seek to answer complex questions based on hypothetical evidence to determine actions for intervention. However, determining the graphical structure of a BN remains a major challenge, especially when modelling a problem under causal assumptions. Solutions to this problem include the automated discovery of BN graphs from data, constructing them based on expert knowledge, or a combination of the two. This paper provides a comprehensive review of combinatoric algorithms proposed for learning BN structure from data, describing 74 algorithms including prototypical, well-established and state-of-the-art approaches. The basic approach of each algorithm is described in consistent terms, and the similarities and differences between them highlighted. Methods of evaluating algorithms and their comparative performance are discussed including the consistency of claims made in the literature. Approaches for dealing with data noise in real-world datasets and incorporating expert knowledge into the learning process are also covered.

Key facts. Cited by 85 papers in the map (data through 7 Oct 2026). Builds on 51 of its 222 references that are in the map. First posted on arXiv 23 Sep 2021.

Builds on

51 of 222 references.

References · 51

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  2. 2021D'ya like DAGs? A Survey on Structure Learning and Causal Discoverycited by 209
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  4. 2013Causal Inference and Causal Explanation with Background Knowledgecited by 168
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38 more
  1. 2013Parameter Priors for Directed Acyclic Graphical Models and the Characterization of Several Probability Distributionscited by 41
  2. 2021The impact of prior knowledge on causal structure learningcited by 35
  3. 2015Partition MCMC for inference on acyclic digraphscited by 33
  4. 2020Towards Scalable Bayesian Learning of Causal DAGscited by 33
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  6. 2020Large-scale empirical validation of Bayesian Network structure learning algorithms with noisy datacited by 29
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  8. 2018Efficient Sampling and Structure Learning of Bayesian Networkscited by 28
  9. 2019Ordering-Based Causal Structure Learning in the Presence of Latent Variablescited by 26
  10. 2013Learning Bayesian Network Structure from Massive Datasets: The "Sparse Candidate" Algorithmcited by 22
  11. 2017Fast Causal Inference with Non-Random Missingness by Test-Wise Deletioncited by 22
  12. 2021Bayesian structure learning and sampling of Bayesian networks with the R package BiDAGcited by 17
  13. 2013Structural Intervention Distance (SID) for Evaluating Causal Graphscited by 14
  14. 2013Properties of Bayesian Belief Network Learning Algorithmscited by 13
  15. 2015A hybrid algorithm for Bayesian network structure learning with application to multi-label learningcited by 12
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 4; 2023: 25; 2024: 18; 2025: 19; 2026: 17.

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  1. 2023Causal Discovery from Temporal Data: An Overview and New Perspectivescited by 43
  2. 2024The Essential Role of Causality in Foundation World Models for Embodied AIcited by 32
  3. 2023A Scale-Invariant Sorting Criterion to Find a Causal Order in Additive Noise Modelscited by 28
  4. 2023Causal Structure Learning Supervised by Large Language Modelcited by 21
  5. 2021FedDAG: Federated DAG Structure Learningcited by 17
  6. 2023CoLiDE: Concomitant Linear DAG Estimationcited by 12
  7. 2024Local Causal Structure Learning in the Presence of Latent Variablescited by 11
  8. 2023DAG Learning on the Permutahedroncited by 9
  9. 2024bnRep: A repository of Bayesian networks from the academic literaturecited by 9
  10. 2021Effective and efficient structure learning with pruning and model averaging strategiescited by 7
  11. 2023Open problems in causal structure learning: A case study of COVID-19 in the UKcited by 7
  12. 2024Adaptive Stream Processing on Edge Devices through Active Inferencecited by 6
38 more
  1. 2025Machine learning interatomic potential can infer electrical responsecited by 6
  2. 2022The Impact of Variable Ordering on Bayesian Network Structure Learningcited by 5
  3. 2023Mitigating Prior Errors in Causal Structure Learning: A Resilient Approach via Bayesian Networkscited by 5
  4. 2023Causal Inference for Banking Finance and Insurance A Surveycited by 5
  5. 2023Learning bounded-degree polytrees with known skeletoncited by 5
  6. 2023Causal discovery using dynamically requested knowledgecited by 5
  7. 2023A Bayesian Take on Gaussian Process Networkscited by 4
  8. 2023Enhancing Interpretability and Generalizability in Extended Isolation Forestscited by 4
  9. 2024ProDAG: Projected Variational Inference for Directed Acyclic Graphscited by 4
  10. 2024Investigating potential causes of Sepsis with Bayesian network structure learningcited by 4
  11. 2022Learning Discrete Directed Acyclic Graphs via Backpropagationcited by 3
  12. 2023Poisoning Network Flow Classifierscited by 3
  13. 2024Using GPT-4 to guide causal machine learningcited by 3
  14. 2024Adaptive Active Inference Agents for Heterogeneous and Lifelong Federated Learningcited by 3
  15. 2022Discovery and density estimation of latent confounders in Bayesian networks with evidence lower boundcited by 2
  16. 2024Weakly-supervised causal discovery based on fuzzy knowledge and complex data complementaritycited by 2
  17. 2025Foundations of a Developmental Design Paradigm for Integrated Continual Learning, Deliberative Behavior, and Comprehensibilitycited by 2
  18. 2025Stable Structure Learning with HC-Stable and Tabu-Stable Algorithmscited by 2
  19. 2025Causality-informed Anomaly Detection in Partially Observable Sensor Networks: Moving beyond Correlationscited by 2
  20. 2026Dynamic Expert-Guided Model Averaging for Causal Discoverycited by 2
  21. 2023Causal Graph Discovery from Self and Mutually Exciting Time Seriescited by 1
  22. 2023Tuning structure learning algorithms with out-of-sample and resampling strategiescited by 1
  23. 2023Fast & Efficient Learning of Bayesian Networks from Data: Knowledge Discovery and Causalitycited by 1
  24. 2023Towards Human-like Perception: Learning Structural Causal Model in Heterogeneous Graphcited by 1
  25. 2024Investigating the validity of structure learning algorithms in identifying risk factors for intervention in patients with diabetescited by 1
  26. 2024Bayesian Functional Connectivity and Graph Convolutional Network for Working Memory Load Classificationcited by 1
  27. 2024ExDAG: an MIQP Algorithm for Learning DAGscited by 1
  28. 2025How Well Does Your Tabular Generator Learn the Structure of Tabular Data?cited by 1
  29. 2025Actionable Counterfactual Explanations Using Bayesian Networks and Path Planning with Applications to Environmental Quality Improvementcited by 1
  30. 2025Surjective Independence of Causal Influences for Local Bayesian Network Structurescited by 1
  31. 2025Incorporating Expert Knowledge into Bayesian Causal Discovery of Mixtures of Directed Acyclic Graphscited by 1
  32. 2025Multi-Dimensional Autoscaling of Stream Processing Services on Edge Devicescited by 1
  33. 2025Differentially Private and Federated Structure Learning in Bayesian Networkscited by 1
  34. 2026Ordering-based Causal Discovery via Generalized Score Matchingcited by 1
  35. 2026On the Number of Conditional Independence Tests in Constraint-based Causal Discoverycited by 1
  36. 2022Parallel Sampling for Efficient High-dimensional Bayesian Network Structure Learningcited by 0
  37. 2023Causal Structural Learning from Time Series: A Convex Optimization Approachcited by 0
  38. 2023Inferential Moments of Uncertain Multivariable Systemscited by 0

50 most cited of 85 All 85 (JSON)