mlsanityData to 14 Oct 2026

Causal Networks: Semantics and Expressiveness

arXiv 1304.2379 ↗First posted 27 Mar 2013cs.AIcited by 67

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Abstract (arXiv)

Dependency knowledge of the form "x is independent of y once z is known" invariably obeys the four graphoid axioms, examples include probabilistic and database dependencies. Often, such knowledge can be represented efficiently with graphical structures such as undirected graphs and directed acyclic graphs (DAGs). In this paper we show that the graphical criterion called d-separation is a sound rule for reading independencies from any DAG based on a causal input list drawn from a graphoid. The rule may be extended to cover DAGs that represent functional dependencies as well as conditional dependencies.

Key facts. Cited by 67 papers in the map (data through 14 Oct 2026). First posted on arXiv 27 Mar 2013.

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Citing papers per year: 2021: 9; 2022: 12; 2023: 18; 2024: 10; 2025: 11; 2026: 7.

67 papers.

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  1. 2022Diffusion Models for Causal Discovery via Topological Orderingcited by 66
  2. 2022Greedy Relaxations of the Sparsest Permutation Algorithmcited by 64
  3. 2021Agent Incentives: A Causal Perspectivecited by 51
  4. 2022Causal Structure Learning: a Combinatorial Perspectivecited by 46
  5. 2023Discovering Causal Relations and Equations from Datacited by 36
  6. 2023Assumption violations in causal discovery and the robustness of score matchingcited by 28
  7. 2022Stochastic Causal Programming for Bounding Treatment Effectscited by 25
  8. 2021A Causal Bandit Approach to Learning Good Atomic Interventions in Presence of Unobserved Confounderscited by 15
  9. 2023Causal models in string diagramscited by 14
  10. 2022The d-separation criterion in Categorical Probabilitycited by 12
  11. 2023Comparing Causal Frameworks: Potential Outcomes, Structural Models, Graphs, and Abstractionscited by 11
  12. 2023No Fair Lunch: A Causal Perspective on Dataset Bias in Machine Learning for Medical Imagingcited by 11
38 more
  1. 2021Context-Specific Causal Discovery for Categorical Data Using Staged Treescited by 10
  2. 2021Finding Valid Adjustments under Non-ignorability with Minimal DAG Knowledgecited by 10
  3. 2022Why Fair Labels Can Yield Unfair Predictions: Graphical Conditions for Introduced Unfairnesscited by 10
  4. 2022Valid Inference After Causal Discoverycited by 10
  5. 2024Rethinking Fair Representation Learning for Performance-Sensitive Taskscited by 8
  6. 2023Heteroscedastic Causal Structure Learningcited by 7
  7. 2024Better Simulations for Validating Causal Discovery with the DAG-Adaptation of the Onion Methodcited by 6
  8. 2024Are Bayesian networks typically faithful?cited by 6
  9. 2022A Complete Criterion for Value of Information in Soluble Influence Diagramscited by 5
  10. 2023Order-based Structure Learning with Normalizing Flowscited by 5
  11. 2024Identifiability Analysis of Linear ODE Systems with Hidden Confounderscited by 5
  12. 2026Causal Representation Learning from General Environments under Nonparametric Mixingcited by 5
  13. 2023Selecting Robust Features for Machine Learning Applications using Multidata Causal Discoverycited by 4
  14. 2023Front-door Adjustment Beyond Markov Equivalence with Limited Graph Knowledgecited by 4
  15. 2024Confounded Budgeted Causal Banditscited by 4
  16. 2025Embracing Discrete Search: A Reasonable Approach to Causal Structure Learningcited by 4
  17. 2021Conditions and Assumptions for Constraint-based Causal Structure Learningcited by 3
  18. 2021Algorithmic Causal Effect Identification with causaleffectcited by 3
  19. 2023Model-based causal feature selection for general response typescited by 3
  20. 2024Identifying Causal Effects Under Functional Dependenciescited by 3
  21. 2025On Different Notions of Redundancy in Conditional-Independence-Based Discovery of Graphical Modelscited by 3
  22. 2025Causal Structure and Representation Learning with Biomedical Applicationscited by 3
  23. 2021The Dual PC Algorithm and the Role of Gaussianity for Structure Learning of Bayesian Networkscited by 2
  24. 2022Formalizing Statistical Causality via Modal Logiccited by 2
  25. 2023On the Independencies Hidden in the Structure of a Probabilistic Logic Programcited by 2
  26. 2025Causal DAG Summarization (Full Version)cited by 2
  27. 2025Causal Ordering for Structure Learning from Time Seriescited by 2
  28. 2021Approximate Implication with d-Separationcited by 1
  29. 2023Learning Personalized Brain Functional Connectivity of MDD Patients from Multiple Sites via Federated Bayesian Networkscited by 1
  30. 2023Causal Razorscited by 1
  31. 2023Axiomatization of Interventional Probability Distributionscited by 1
  32. 2024DAGnosis: Localized Identification of Data Inconsistencies using Structurescited by 1
  33. 2024Enabling Causal Discovery in Post-Nonlinear Models with Normalizing Flowscited by 1
  34. 2024Boosting Efficiency in Task-Agnostic Exploration through Causal Knowledgecited by 1
  35. 2025Meta-Dependence in Conditional Independence Testingcited by 1
  36. 2025Lower Bounds on the Size of Markov Equivalence Classescited by 1
  37. 2025A Primer on Causal and Statistical Dataset Biases for Fair and Robust Image Analysiscited by 1
  38. 2021Modelling Major Disease Outbreaks in the 21st Century: A Causal Approachcited by 0

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