mlsanityData to 14 Oct 2026

CAM: Causal additive models, high-dimensional order search and penalized regression

arXiv 1310.1533 ↗First posted 6 Oct 2013stat.ME cs.LG stat.MLcited by 178

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Abstract (arXiv)

We develop estimation for potentially high-dimensional additive structural equation models. A key component of our approach is to decouple order search among the variables from feature or edge selection in a directed acyclic graph encoding the causal structure. We show that the former can be done with nonregularized (restricted) maximum likelihood estimation while the latter can be efficiently addressed using sparse regression techniques. Thus, we substantially simplify the problem of structure search and estimation for an important class of causal models. We establish consistency of the (restricted) maximum likelihood estimator for low- and high-dimensional scenarios, and we also allow for misspecification of the error distribution. Furthermore, we develop an efficient computational algorithm which can deal with many variables, and the new method's accuracy and performance is illustrated on simulated and real data.

Key facts. Cited by 178 papers in the map (data through 14 Oct 2026). First posted on arXiv 6 Oct 2013.

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Citing papers per year: 2021: 18; 2022: 26; 2023: 38; 2024: 36; 2025: 24; 2026: 36.

178 papers.

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  1. 2021D'ya like DAGs? A Survey on Structure Learning and Causal Discoverycited by 211
  2. 2021Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Gamecited by 161
  3. 2022DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterizationcited by 140
  4. 2022Score matching enables causal discovery of nonlinear additive noise modelscited by 111
  5. 2022Deep End-to-end Causal Inferencecited by 95
  6. 2022Diffusion Models for Causal Discovery via Topological Orderingcited by 66
  7. 2023A Survey on Causal Discovery: Theory and Practicecited by 63
  8. 2021gCastle: A Python Toolbox for Causal Discoverycited by 61
  9. 2022On the Identifiability and Estimation of Causal Location-Scale Noise Modelscited by 56
  10. 2021Ordering-Based Causal Discovery with Reinforcement Learningcited by 55
  11. 2021DAGs with No Curl: An Efficient DAG Structure Learning Approachcited by 53
  12. 2022Differentiable DAG Samplingcited by 47
38 more
  1. 2022Causal Structure Learning: a Combinatorial Perspectivecited by 46
  2. 2023Scalable Causal Discovery with Score Matchingcited by 45
  3. 2021Variational Causal Networks: Approximate Bayesian Inference over Causal Structurescited by 43
  4. 2023Causal Discovery with Score Matching on Additive Models with Arbitrary Noisecited by 43
  5. 2023A Survey on Causal Discovery Methods for I.I.D. and Time Series Datacited by 35
  6. 2023Causal Representation Learning Made Identifiable by Grouping of Observational Variablescited by 32
  7. 2023Stable Differentiable Causal Discoverycited by 31
  8. 2023A Scale-Invariant Sorting Criterion to Find a Causal Order in Additive Noise Modelscited by 28
  9. 2023Assumption violations in causal discovery and the robustness of score matchingcited by 28
  10. 2021Data Generating Process to Evaluate Causal Discovery Techniques for Time Series Datacited by 22
  11. 2022Differentiable Causal Discovery Under Latent Interventionscited by 21
  12. 2024Sample, estimate, aggregate: A recipe for causal discovery foundation modelscited by 21
  13. 2023Automated Scientific Discovery: From Equation Discovery to Autonomous Discovery Systemscited by 19
  14. 2023textttcausalAssembly: Generating Realistic Production Data for Benchmarking Causal Discoverycited by 18
  15. 2024The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applicationscited by 18
  16. 2021FedDAG: Federated DAG Structure Learningcited by 17
  17. 2022Optimal estimation of Gaussian DAG modelscited by 17
  18. 2023Optimizing NOTEARS Objectives via Topological Swapscited by 17
  19. 2024Standardizing Structural Causal Modelscited by 17
  20. 2024Adjustment Identification Distance: A gadjid for Causal Structure Learningcited by 16
  21. 2023On Learning Necessary and Sufficient Causal Graphscited by 14
  22. 2022Distributed Learning of Generalized Linear Causal Networkscited by 13
  23. 2023Computably Continuous Reinforcement-Learning Objectives are PAC-learnablecited by 13
  24. 2023CoLiDE: Concomitant Linear DAG Estimationcited by 13
  25. 2024Ordering-Based Causal Discovery for Linear and Nonlinear Relationscited by 13
  26. 2022Characterization and Greedy Learning of Gaussian Structural Causal Models under Unknown Interventionscited by 12
  27. 2024Recursive Causal Discoverycited by 12
  28. 2021Structure learning in polynomial time: Greedy algorithms, Bregman information, and exponential familiescited by 11
  29. 2022A Meta-Reinforcement Learning Algorithm for Causal Discoverycited by 11
  30. 2022GFlowCausal: Generative Flow Networks for Causal Discoverycited by 11
  31. 2023Toward Falsifying Causal Graphs Using a Permutation-Based Testcited by 11
  32. 2023Federated Causality Learning with Explainable Adaptive Optimizationcited by 11
  33. 2024Demystifying amortized causal discovery with transformerscited by 11
  34. 2021Typing assumptions improve identification in causal discoverycited by 10
  35. 2023Additive Causal Bandits with Unknown Graphcited by 10
  36. 2024Score matching through the roof: linear, nonlinear, and latent variables causal discoverycited by 10
  37. 2021Structure Learning for Directed Treescited by 9
  38. 2023DAG Learning on the Permutahedroncited by 9

50 most cited of 178 All 178 (JSON)