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A Transformational Characterization of Equivalent Bayesian Network Structures

arXiv 1302.4938 ↗First posted 20 Feb 2013cs.AIcited by 41

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Abstract (arXiv)

We present a simple characterization of equivalent Bayesian network structures based on local transformations. The significance of the characterization is twofold. First, we are able to easily prove several new invariant properties of theoretical interest for equivalent structures. Second, we use the characterization to derive an efficient algorithm that identifies all of the compelled edges in a structure. Compelled edge identification is of particular importance for learning Bayesian network structures from data because these edges indicate causal relationships when certain assumptions hold.

Key facts. Cited by 41 papers in the map (data through 7 Oct 2026). First posted on arXiv 20 Feb 2013.

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Citing papers per year: 2021: 5; 2022: 8; 2023: 14; 2024: 7; 2025: 5; 2026: 2.

41 papers.

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  1. 2021Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Gamecited by 159
  2. 2022Greedy Relaxations of the Sparsest Permutation Algorithmcited by 63
  3. 2022Causal Structure Learning: a Combinatorial Perspectivecited by 46
  4. 2023Fast Scalable and Accurate Discovery of DAGs Using the Best Order Score Search and Grow-Shrink Treescited by 38
  5. 2023Learning nonparametric latent causal graphs with unknown interventionscited by 34
  6. 2023A Versatile Causal Discovery Framework to Allow Causally-Related Hidden Variablescited by 33
  7. 2022Verification and search algorithms for causal DAGscited by 18
  8. 2024Causal Discovery with Fewer Conditional Independence Testscited by 13
  9. 2022Characterization and Greedy Learning of Gaussian Structural Causal Models under Unknown Interventionscited by 12
  10. 2023Subset verification and search algorithms for causal DAGscited by 12
  11. 2024The Causal Chambers: Real Physical Systems as a Testbed for AI Methodologycited by 12
  12. 2021Benchpress: A Scalable and Versatile Workflow for Benchmarking Structure Learning Algorithmscited by 11
29 more
  1. 2023Active causal structure learning with advicecited by 10
  2. 2023Efficient Enumeration of Markov Equivalent DAGscited by 6
  3. 2022A Transformational Characterization of Unconditionally Equivalent Bayesian Networkscited by 4
  4. 2026Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learningcited by 4
  5. 2023New metrics and search algorithms for weighted causal DAGscited by 3
  6. 2023Meek Separators and Their Applications in Targeted Causal Discoverycited by 3
  7. 2025Dynamic Causal Structure Discovery and Causal Effect Estimationcited by 3
  8. 2021Universal Lower Bound for Learning Causal DAGs with Atomic Interventionscited by 2
  9. 2023Causal structure learning with momentum: Sampling distributions over Markov Equivalence Classes of DAGscited by 2
  10. 2023Bayesian causal discovery from unknown general interventionscited by 2
  11. 2024Causal Discovery under Off-Target Interventionscited by 2
  12. 2025Higher-Order Causal Structure Learning with Additive Modelscited by 2
  13. 2023Causal Razorscited by 1
  14. 2023Practical Algorithms for Orientations of Partially Directed Graphical Modelscited by 1
  15. 2023A Fixed-Parameter Tractable Algorithm for Counting Markov Equivalence Classes with the same Skeletoncited by 1
  16. 2023Extracting the Multiscale Causal Backbone of Brain Dynamicscited by 1
  17. 2024Quotient Normalized Maximum Likelihood Criterion for Learning Bayesian Network Structurescited by 1
  18. 2025Heterogeneous Causal Discovery of Repeated Undesirable Health Outcomescited by 1
  19. 2025Lower Bounds on the Size of Markov Equivalence Classescited by 1
  20. 2025Less Greedy Equivalence Searchcited by 1
  21. 2021Parameter Priors for Directed Acyclic Graphical Models and the Characterization of Several Probability Distributionscited by 0
  22. 2021Causal KL: Evaluating Causal Discoverycited by 0
  23. 2022Gaussian mixture modeling of nodes in Bayesian network according to maximal parental cliquescited by 0
  24. 2022Fast Causal Orientation Learning in Directed Acyclic Graphscited by 0
  25. 2022Counting Markov Equivalent Directed Acyclic Graphs Consistent with Background Knowledgecited by 0
  26. 2024Membership Testing in Markov Equivalence Classes via Independence Query Oraclescited by 0
  27. 2024A Full DAG Score-Based Algorithm for Learning Causal Bayesian Networks with Latent Confounderscited by 0
  28. 2024Causal Discovery in Recommender Systems: Example and Discussioncited by 0
  29. 2026Leveraging heterogeneity for identifiability: Bayesian order-based learning of multiple DAGscited by 0