mlsanityData to 7 Oct 2026

Causal Structure Learning: a Combinatorial Perspective

arXiv 2206.01152 ↗First posted 2 Jun 2022stat.ME cs.LGcited by 46

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Abstract (arXiv)

In this review, we discuss approaches for learning causal structure from data, also called causal discovery. In particular, we focus on approaches for learning directed acyclic graphs (DAGs) and various generalizations which allow for some variables to be unobserved in the available data. We devote special attention to two fundamental combinatorial aspects of causal structure learning. First, we discuss the structure of the search space over causal graphs. Second, we discuss the structure of equivalence classes over causal graphs, i.e., sets of graphs which represent what can be learned from observational data alone, and how these equivalence classes can be refined by adding interventional data.

Key facts. Cited by 46 papers in the map (data through 7 Oct 2026). Builds on 85 of its 204 references that are in the map. First posted on arXiv 2 Jun 2022.

Builds on

85 of 204 references.

References · 85

  1. 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 745
  2. 2019DAG-GNN: DAG Structure Learning with Graph Neural Networkscited by 329
  3. 2019Gradient-Based Neural DAG Learningcited by 227
  4. 2020Differentiable Causal Discovery from Interventional Datacited by 218
  5. 2013CAM: Causal additive models, high-dimensional order search and penalized regressioncited by 175
  6. 2013Causal Inference and Causal Explanation with Background Knowledgecited by 168
  7. 2013Causal Inference in the Presence of Latent Variables and Selection Biascited by 165
  8. 2017Invariant Causal Prediction for Nonlinear Modelscited by 140
  9. 2016Foundations of Structural Causal Models with Cycles and Latent Variablescited by 134
  10. 2022Semiparametric doubly robust targeted double machine learning: a reviewcited by 129
  11. 2019Learning Neural Causal Models from Unknown Interventionscited by 113
  12. 2021DiBS: Differentiable Bayesian Structure Learningcited by 105
38 more
  1. 2016Causal Bandits: Learning Good Interventions via Causal Inferencecited by 100
  2. 2019D-VAE: A Variational Autoencoder for Directed Acyclic Graphscited by 98
  3. 2017Causal Structure Learningcited by 84
  4. 2017Permutation-based Causal Inference Algorithms with Interventionscited by 78
  5. 2017Approximate Kernel-based Conditional Independence Tests for Fast Non-Parametric Causal Discoverycited by 76
  6. 2018Characterizing and Learning Equivalence Classes of Causal DAGs under Interventionscited by 76
  7. 2019Permutation-Based Causal Structure Learning with Unknown Intervention Targetscited by 69
  8. 2013Causal Networks: Semantics and Expressivenesscited by 67
  9. 2016Structure Learning in Graphical Modelingcited by 66
  10. 2020Differentiable Causal Discovery Under Unmeasured Confoundingcited by 56
  11. 2021Learning latent causal graphs via mixture oraclescited by 55
  12. 2013Causal Discovery from Changescited by 52
  13. 2019ABCD-Strategy: Budgeted Experimental Design for Targeted Causal Structure Discoverycited by 52
  14. 2022Interventions, Where and How? Experimental Design for Causal Models at Scalecited by 49
  15. 2013Learning Sparse Causal Models is not NP-hardcited by 48
  16. 2014Constraint-based Causal Discovery from Multiple Interventions over Overlapping Variable Setscited by 48
  17. 2015High-dimensional consistency in score-based and hybrid structure learningcited by 44
  18. 2017Cost-Optimal Learning of Causal Graphscited by 44
  19. 2013Parameter Priors for Directed Acyclic Graphical Models and the Characterization of Several Probability Distributionscited by 41
  20. 2013A Transformational Characterization of Equivalent Bayesian Network Structurescited by 41
  21. 2017Nested Markov Properties for Acyclic Directed Mixed Graphscited by 38
  22. 2017Budgeted Experiment Design for Causal Structure Learningcited by 38
  23. 2020Active Structure Learning of Causal DAGs via Directed Clique Treecited by 38
  24. 2020Budgeted and Non-budgeted Causal Banditscited by 38
  25. 2015backShift: Learning causal cyclic graphs from unknown shift interventionscited by 37
  26. 2021Causal Bandits with Unknown Graph Structurecited by 37
  27. 2018Constraint-based Causal Discovery for Non-Linear Structural Causal Models with Cycles and Latent Confounderscited by 35
  28. 2015Partition MCMC for inference on acyclic digraphscited by 33
  29. 2020Constraint-Based Causal Discovery using Partial Ancestral Graphs in the presence of Cyclescited by 31
  30. 2018Learning and Testing Causal Models with Interventionscited by 29
  31. 2016Entropic Causal Inferencecited by 27
  32. 2017Learning Identifiable Gaussian Bayesian Networks in Polynomial Time and Sample Complexitycited by 27
  33. 2015Margins of discrete Bayesian networkscited by 26
  34. 2019Ordering-Based Causal Structure Learning in the Presence of Latent Variablescited by 26
  35. 2018Experimental Design for Cost-Aware Learning of Causal Graphscited by 25
  36. 2018Causal Modeling of Dynamical Systemscited by 24
  37. 2018High-Dimensional Causal Discovery Under non-Gaussianitycited by 24
  38. 2020Causal Structure Discovery from Distributions Arising from Mixtures of DAGscited by 24

50 most cited of 85 All 85 (JSON)

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Cited by year (2026 to 7 Oct)

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

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  1. 2023Nonparametric Identifiability of Causal Representations from Unknown Interventionscited by 105
  2. 2023Learning Linear Causal Representations from Interventions under General Nonlinear Mixingcited by 92
  3. 2022Linear Causal Disentanglement via Interventionscited by 84
  4. 2023Identifiability Guarantees for Causal Disentanglement from Soft Interventionscited by 84
  5. 2024On the Origins of Linear Representations in Large Language Modelscited by 76
  6. 2023Causal Discovery from Temporal Data: An Overview and New Perspectivescited by 43
  7. 2024Learning Interpretable Concepts: Unifying Causal Representation Learning and Foundation Modelscited by 29
  8. 2022Causal Abstraction with Soft Interventionscited by 23
  9. 2023Counterfactual (Non-)identifiability of Learned Structural Causal Modelscited by 17
  10. 2024Standardizing Structural Causal Modelscited by 17
  11. 2024Causal Discovery with Fewer Conditional Independence Testscited by 13
  12. 2023Local Causal Discovery for Estimating Causal Effectscited by 10
34 more
  1. 2023An Interventional Perspective on Identifiability in Gaussian LTI Systems with Independent Component Analysiscited by 9
  2. 2024C2P: Featuring Large Language Models with Causal Reasoningcited by 8
  3. 2023Heteroscedastic Causal Structure Learningcited by 6
  4. 2024Effective Bayesian Causal Inference via Structural Marginalisation and Autoregressive Orderscited by 6
  5. 2025Overcoming Fairness Trade-offs via Pre-processing: A Causal Perspectivecited by 5
  6. 2024Investigating potential causes of Sepsis with Bayesian network structure learningcited by 4
  7. 2023dotears: Scalable, consistent DAG estimation using observational and interventional datacited by 3
  8. 2023Differentiable Bayesian Structure Learning with Acyclicity Assurancecited by 3
  9. 2023Meek Separators and Their Applications in Targeted Causal Discoverycited by 3
  10. 2023Learned Causal Method Predictioncited by 3
  11. 2023Causal Discovery in Mixtures of Populationscited by 3
  12. 2024Optimal estimation of Gaussian (poly)treescited by 3
  13. 2025Measure-Theoretic Anti-Causal Representation Learningcited by 3
  14. 2024Causal Imputation for Counterfactual SCMs: Bridging Graphs and Latent Factor Modelscited by 2
  15. 2024Greedy equivalence search for nonparametric graphical modelscited by 2
  16. 2025DAG DECORation: Continuous Optimization for Structure Learning under Hidden Confoundingcited by 2
  17. 2024Score-matching-based Structure Learning for Temporal Data on Networkscited by 1
  18. 2025Meta-Dependence in Conditional Independence Testingcited by 1
  19. 2025Probabilistic and Causal Satisfiability: Constraining the Modelcited by 1
  20. 2026Catastrophic Compositional Generation: Why Vanilla Diffusion Models Fail to Extrapolatecited by 1
  21. 2023Learning Linear Gaussian Polytree Models with Interventionscited by 0
  22. 2024Continual Learning of Nonlinear Independent Representationscited by 0
  23. 2024Celcomen: spatial causal disentanglement for single-cell and tissue perturbation modelingcited by 0
  24. 2024Working Paper: Active Causal Structure Learning with Latent Variables: Towards Learning to Detour in Autonomous Robotscited by 0
  25. 2025Uncovering Bias Mechanisms in Observational Studiescited by 0
  26. 2025Learning Granger Causality under Latent Confounding via Intervention-Induced Heterogeneitycited by 0
  27. 2025QML-HCS: A Hypercausal Quantum Machine Learning Framework for Non-Stationary Environmentscited by 0
  28. 2026Causal Discovery Should Embrace the Wisdom of the Crowdcited by 0
  29. 2026Learning Causal Structure of Time Series using Best Order Score Searchcited by 0
  30. 2026Data Augmentation via Causal-Residual Bootstrappingcited by 0
  31. 2026Relaxing Faithfulness with Intervention-Only Causal Discoverycited by 0
  32. 2026SVI-DAG: A Structured Variational Inference Approach to Bayesian Causal Discoverycited by 0
  33. 2026Nonnegative DAG Learning via Concomitant Estimationcited by 0
  34. 2026Structure-agnostic Causal Representation Learningcited by 0