mlsanityData to 14 Oct 2026

Score matching enables causal discovery of nonlinear additive noise models

arXiv 2203.04413 ↗First posted 8 Mar 2022cs.LG stat.MLcited by 111

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Abstract (arXiv)

This paper demonstrates how to recover causal graphs from the score of the data distribution in non-linear additive (Gaussian) noise models. Using score matching algorithms as a building block, we show how to design a new generation of scalable causal discovery methods. To showcase our approach, we also propose a new efficient method for approximating the score's Jacobian, enabling to recover the causal graph. Empirically, we find that the new algorithm, called SCORE, is competitive with state-of-the-art causal discovery methods while being significantly faster.

Key facts. Cited by 111 papers in the map (data through 14 Oct 2026). Builds on 20 of its 47 references that are in the map. First posted on arXiv 8 Mar 2022.

Builds on

20 of 47 references.

References · 20

  1. 2020Score-Based Generative Modeling through Stochastic Differential Equationscited by 9,122
  2. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,101
  3. 2020Improved Techniques for Training Score-Based Generative Modelscited by 1,043
  4. 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 752
  5. 2019Sliced Score Matching: A Scalable Approach to Density and Score Estimationcited by 384
  6. 2013Causal Discovery with Continuous Additive Noise Modelscited by 255
  7. 2016A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluationcited by 236
  8. 2019Gradient-Based Neural DAG Learningcited by 227
  9. 2013CAM: Causal additive models, high-dimensional order search and penalized regressioncited by 178
  10. 2019Causal Discovery with Reinforcement Learningcited by 145
  11. 2020Amortized Causal Discovery: Learning to Infer Causal Graphs from Time-Series Datacited by 100
  12. 2013High-dimensional learning of linear causal networks via inverse covariance estimationcited by 87
8 more
  1. 2017Gradient Estimators for Implicit Modelscited by 58
  2. 2019Minimum Stein Discrepancy Estimatorscited by 57
  3. 2021Ordering-Based Causal Discovery with Reinforcement Learningcited by 55
  4. 2021Score-Based Generative Classifierscited by 53
  5. 2017Learning linear structural equation models in polynomial time and sample complexitycited by 51
  6. 2021Hessian Estimation via Stein's Identity in Black-Box Problemscited by 8
  7. 2013An Algorithm for the Construction of Bayesian Network Structures from Datacited by 5
  8. 2013Optimizing Causal Orderings for Generating DAGs from Datacited by 5

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2022: 6; 2023: 25; 2024: 30; 2025: 25; 2026: 25.

111 papers.

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  1. 2022Diffusion Models for Causal Discovery via Topological Orderingcited by 66
  2. 2023Score-based Causal Representation Learning with Interventionscited by 49
  3. 2023Causal Order: The Key to Leveraging Imperfect Experts in Causal Inferencecited by 48
  4. 2023Scalable Causal Discovery with Score Matchingcited by 45
  5. 2023Causal Discovery with Score Matching on Additive Models with Arbitrary Noisecited by 43
  6. 2023General Identifiability and Achievability for Causal Representation Learningcited by 34
  7. 2024Integrating Large Language Models in Causal Discovery: A Statistical Causal Approachcited by 32
  8. 2023Stable Differentiable Causal Discoverycited by 31
  9. 2023A Scale-Invariant Sorting Criterion to Find a Causal Order in Additive Noise Modelscited by 28
  10. 2023Assumption violations in causal discovery and the robustness of score matchingcited by 28
  11. 2024A Meta-Learning Approach to Bayesian Causal Discoverycited by 22
  12. 2023textttcausalAssembly: Generating Realistic Production Data for Benchmarking Causal Discoverycited by 18
38 more
  1. 2024Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processescited by 18
  2. 2024The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applicationscited by 18
  3. 2025Proper scoring rules for estimation and forecast evaluationcited by 18
  4. 2023Sample Complexity Bounds for Score-Matching: Causal Discovery and Generative Modelingcited by 16
  5. 2024Adjustment Identification Distance: A gadjid for Causal Structure Learningcited by 16
  6. 2023On Learning Necessary and Sufficient Causal Graphscited by 14
  7. 2022Independence Testing-Based Approach to Causal Discovery under Measurement Error and Linear Non-Gaussian Modelscited by 13
  8. 2024Ordering-Based Causal Discovery for Linear and Nonlinear Relationscited by 13
  9. 2025Towards Interpretable Deep Generative Models via Causal Representation Learningcited by 13
  10. 2023Toward Falsifying Causal Graphs Using a Permutation-Based Testcited by 11
  11. 2024Demystifying amortized causal discovery with transformerscited by 11
  12. 2024Exploring Multi-Modal Data with Tool-Augmented LLM Agents for Precise Causal Discoverycited by 11
  13. 2022Novel Ordering-based Approaches for Causal Structure Learning in the Presence of Unobserved Variablescited by 10
  14. 2022Disentangling Causal Effects from Sets of Interventions in the Presence of Unobserved Confounderscited by 10
  15. 2022Instrumental Variables in Causal Inference and Machine Learning: A Surveycited by 10
  16. 2023Emerging Synergies in Causality and Deep Generative Models: A Surveycited by 10
  17. 2024Amortized Active Causal Induction with Deep Reinforcement Learningcited by 10
  18. 2024Score matching through the roof: linear, nonlinear, and latent variables causal discoverycited by 10
  19. 2024Causal Agent based on Large Language Modelcited by 10
  20. 2023DAG Learning on the Permutahedroncited by 9
  21. 2023Local Discovery by Partitioning: Polynomial-Time Causal Discovery Around Exposure-Outcome Pairscited by 9
  22. 2023Heteroscedastic Causal Structure Learningcited by 7
  23. 2024A Skewness-Based Criterion for Addressing Heteroscedastic Noise in Causal Discoverycited by 7
  24. 2024Identifiability Guarantees for Causal Disentanglement from Purely Observational Datacited by 7
  25. 2025Learning General Causal Structures with Hidden Dynamic Process for Climate Analysiscited by 7
  26. 2025CAUSAL3D: A Comprehensive Benchmark for Causal Learning from Visual Datacited by 7
  27. 2024Scalable and Flexible Causal Discovery with an Efficient Test for Adjacencycited by 6
  28. 2024Continuous Bayesian Model Selection for Multivariate Causal Discoverycited by 6
  29. 2025Distinguishing Cause from Effect with Causal Velocity Modelscited by 6
  30. 2023iSCAN: Identifying Causal Mechanism Shifts among Nonlinear Additive Noise Modelscited by 5
  31. 2023Order-based Structure Learning with Normalizing Flowscited by 5
  32. 2024Hybrid Top-Down Global Causal Discovery with Local Search for Linear and Nonlinear Additive Noise Modelscited by 5
  33. 2024Deriving Causal Order from Single-Variable Interventions: Guarantees & Algorithmcited by 5
  34. 2025Nonlinear Causal Discovery for Grouped Datacited by 5
  35. 2026Causal Representation Learning from General Environments under Nonparametric Mixingcited by 5
  36. 2023Learning Causal Graphs via Monotone Triangular Transport Mapscited by 4
  37. 2023Shortcuts for causal discovery of nonlinear models by score matchingcited by 4
  38. 2025Since Faithfulness Fails: The Performance Limits of Neural Causal Discoverycited by 4

50 most cited of 111 All 111 (JSON)