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Causal Discovery with Continuous Additive Noise Models

arXiv 1309.6779 ↗First posted 26 Sep 2013stat.MLcited by 252

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Abstract (arXiv)

We consider the problem of learning causal directed acyclic graphs from an observational joint distribution. One can use these graphs to predict the outcome of interventional experiments, from which data are often not available. We show that if the observational distribution follows a structural equation model with an additive noise structure, the directed acyclic graph becomes identifiable from the distribution under mild conditions. This constitutes an interesting alternative to traditional methods that assume faithfulness and identify only the Markov equivalence class of the graph, thus leaving some edges undirected. We provide practical algorithms for finitely many samples, RESIT (Regression with Subsequent Independence Test) and two methods based on an independence score. We prove that RESIT is correct in the population setting and provide an empirical evaluation.

Key facts. Cited by 252 papers in the map (data through 7 Oct 2026). First posted on arXiv 26 Sep 2013.

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Citing papers per year: 2019: 1; 2020: 0; 2021: 24; 2022: 34; 2023: 58; 2024: 46; 2025: 47; 2026: 42.

252 papers.

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  1. 2019Causal Confusion in Imitation Learningcited by 286
  2. 2021Towards Causal Representation Learningcited by 207
  3. 2022DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterizationcited by 135
  4. 2022Score matching enables causal discovery of nonlinear additive noise modelscited by 108
  5. 2021A Clarification of the Nuances in the Fairness Metrics Landscapecited by 98
  6. 2021Independent mechanism analysis, a new concept?cited by 96
  7. 2022Deep End-to-end Causal Inferencecited by 93
  8. 2021BCD Nets: Scalable Variational Approaches for Bayesian Causal Discoverycited by 68
  9. 2022Diffusion Models for Causal Discovery via Topological Orderingcited by 64
  10. 2023Identifiability of latent-variable and structural-equation models: from linear to nonlinearcited by 58
  11. 2022On the Identifiability and Estimation of Causal Location-Scale Noise Modelscited by 56
  12. 2021Ordering-Based Causal Discovery with Reinforcement Learningcited by 55
38 more
  1. 2021Learning latent causal graphs via mixture oraclescited by 55
  2. 2021DAGs with No Curl: An Efficient DAG Structure Learning Approachcited by 53
  3. 2022Differentiable DAG Samplingcited by 46
  4. 2023Causal Discovery from Temporal Data: An Overview and New Perspectivescited by 43
  5. 2025CausalPFN: Amortized Causal Effect Estimation via In-Context Learningcited by 43
  6. 2022Causal de Finetti: On the Identification of Invariant Causal Structure in Exchangeable Datacited by 42
  7. 2023Counterfactual Identifiability of Bijective Causal Modelscited by 42
  8. 2023Causal Discovery with Score Matching on Additive Models with Arbitrary Noisecited by 41
  9. 2022From Statistical to Causal Learningcited by 40
  10. 2022Identifying Patient-Specific Root Causes with the Heteroscedastic Noise Modelcited by 38
  11. 2022Active Bayesian Causal Inferencecited by 34
  12. 2022Identifying Weight-Variant Latent Causal Modelscited by 33
  13. 2023BayesDAG: Gradient-Based Posterior Inference for Causal Discoverycited by 33
  14. 2021Towards Federated Bayesian Network Structure Learning with Continuous Optimizationcited by 31
  15. 2023Causal Representation Learning Made Identifiable by Grouping of Observational Variablescited by 30
  16. 2023Stable Differentiable Causal Discoverycited by 30
  17. 2024Unifying Causal Representation Learning with the Invariance Principlecited by 30
  18. 2023Assumption violations in causal discovery and the robustness of score matchingcited by 28
  19. 2023Identifiable Latent Polynomial Causal Models Through the Lens of Changecited by 23
  20. 2022MissDAG: Causal Discovery in the Presence of Missing Data with Continuous Additive Noise Modelscited by 21
  21. 2022Counterfactual Fairness with Partially Known Causal Graphcited by 20
  22. 2023Causal Deep Learningcited by 20
  23. 2024Root Cause Analysis of Outliers with Missing Structural Knowledgecited by 19
  24. 2023Automated Scientific Discovery: From Equation Discovery to Autonomous Discovery Systemscited by 18
  25. 2023textttcausalAssembly: Generating Realistic Production Data for Benchmarking Causal Discoverycited by 18
  26. 2023Counterfactual (Non-)identifiability of Learned Structural Causal Modelscited by 17
  27. 2023Estimating Treatment Effects from Irregular Time Series Observations with Hidden Confounderscited by 17
  28. 2023Optimizing NOTEARS Objectives via Topological Swapscited by 17
  29. 2024The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applicationscited by 17
  30. 2024Adjustment Identification Distance: A gadjid for Causal Structure Learningcited by 16
  31. 2023Causal Reasoning in the Presence of Latent Confounders via Neural ADMG Learningcited by 15
  32. 2023Sample Complexity Bounds for Score-Matching: Causal Discovery and Generative Modelingcited by 15
  33. 2022Optimal estimation of Gaussian DAG modelscited by 14
  34. 2023On Learning Necessary and Sufficient Causal Graphscited by 14
  35. 2022Distributed Learning of Generalized Linear Causal Networkscited by 13
  36. 2023Computably Continuous Reinforcement-Learning Objectives are PAC-learnablecited by 13
  37. 2024ADAM: An Embodied Causal Agent in Open-World Environmentscited by 13
  38. 2023DRCFS: Doubly Robust Causal Feature Selectioncited by 12

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