mlsanityData to 7 Oct 2026

Scalable Causal Discovery with Score Matching

arXiv 2304.03382 ↗First posted 6 Apr 2023cs.LG stat.MLcited by 42

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Abstract (arXiv)

This paper demonstrates how to discover the whole causal graph from the second derivative of the log-likelihood in observational non-linear additive Gaussian noise models. Leveraging scalable machine learning approaches to approximate the score function nabla log p(X), we extend the work of Rolland et al. (2022) that only recovers the topological order from the score and requires an expensive pruning step removing spurious edges among those admitted by the ordering. Our analysis leads to DAS (acronym for Discovery At Scale), a practical algorithm that reduces the complexity of the pruning by a factor proportional to the graph size. In practice, DAS achieves competitive accuracy with current state-of-the-art while being over an order of magnitude faster. Overall, our approach enables principled and scalable causal discovery, significantly lowering the compute bar.

Key facts. Cited by 42 papers in the map (data through 7 Oct 2026). Builds on 8 of its 38 references that are in the map. First posted on arXiv 6 Apr 2023.

Builds on

8 of 38 references.

References · 8

  1. 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 745
  2. 2019Gradient-Based Neural DAG Learningcited by 227
  3. 2013CAM: Causal additive models, high-dimensional order search and penalized regressioncited by 175
  4. 2022Score matching enables causal discovery of nonlinear additive noise modelscited by 108
  5. 2020Amortized Causal Discovery: Learning to Infer Causal Graphs from Time-Series Datacited by 99
  6. 2017Inference via low-dimensional couplingscited by 43
  7. 2017Beyond normality: Learning sparse probabilistic graphical models in the non-Gaussian settingcited by 15
  8. 2021Obtaining Causal Information by Merging Datasets with MAXENTcited by 9

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 7; 2024: 13; 2025: 7; 2026: 15.

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  1. 2023General Identifiability and Achievability for Causal Representation Learningcited by 34
  2. 2023Assumption violations in causal discovery and the robustness of score matchingcited by 28
  3. 2023textttcausalAssembly: Generating Realistic Production Data for Benchmarking Causal Discoverycited by 18
  4. 2024Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processescited by 18
  5. 2024Identifiable Exchangeable Mechanisms for Causal Structure and Representation Learningcited by 16
  6. 2023Sample Complexity Bounds for Score-Matching: Causal Discovery and Generative Modelingcited by 15
  7. 2024DCILP: A Distributed Approach for Large-Scale Causal Structure Learningcited by 8
  8. 2024Score matching through the roof: linear, nonlinear, and latent variables causal discoverycited by 8
  9. 2024A Skewness-Based Criterion for Addressing Heteroscedastic Noise in Causal Discoverycited by 7
  10. 2024Identifiability Guarantees for Causal Disentanglement from Purely Observational Datacited by 7
  11. 2025Distinguishing Cause from Effect with Causal Velocity Modelscited by 6
  12. 2024Hybrid Top-Down Global Causal Discovery with Local Search for Linear and Nonlinear Additive Noise Modelscited by 5
30 more
  1. 2024Scalable and Flexible Causal Discovery with an Efficient Test for Adjacencycited by 5
  2. 2023Learning Causal Graphs via Monotone Triangular Transport Mapscited by 4
  3. 2023Shortcuts for causal discovery of nonlinear models by score matchingcited by 4
  4. 2024AcceleratedLiNGAM: Learning Causal DAGs at the speed of GPUscited by 4
  5. 2026Causal Representation Learning from General Environments under Nonparametric Mixingcited by 4
  6. 2023Differentiable Bayesian Structure Learning with Acyclicity Assurancecited by 3
  7. 2024Cross-validating causal discovery via Leave-One-Variable-Outcited by 2
  8. 2026DAG-FM: A Foundation Model for Causal Discovery under Heterogeneous Causal Mechanismscited by 2
  9. 2024LoSAM: Local Search in Additive Noise Models with Mixed Mechanisms and General Noise for Global Causal Discoverycited by 1
  10. 2024Causal Order Discovery based on Monotonic SCMscited by 1
  11. 2024Score-matching-based Structure Learning for Temporal Data on Networkscited by 1
  12. 2025Causal Discovery via Bayesian Optimizationcited by 1
  13. 2025Your Assumed DAG is Wrong and Here's How To Deal With Itcited by 1
  14. 2025When Additive Noise Meets Unobserved Mediators: Bivariate Denoising Diffusion for Causal Discoverycited by 1
  15. 2025Causal Ordering for Structure Learning from Time Seriescited by 1
  16. 2026Ordering-based Causal Discovery via Generalized Score Matchingcited by 1
  17. 2026Learning Causal Orderings for In-Context Tabular Predictioncited by 1
  18. 2026Order-based Causal Discovery for Multistage Processescited by 1
  19. 2025Estimating Treatment Effects with Independent Component Analysiscited by 0
  20. 2025On the Identifiability of Causal Graphs with the Invariance Principlecited by 0
  21. 2026Efficient Causal Structure Learning via Modular Subgraph Integrationcited by 0
  22. 2026Causal Graph Learning via Distributional Invariance of Cause-Effect Relationshipcited by 0
  23. 2026Sparse Additive Model Pruning for Order-Based Causal Structure Learningcited by 0
  24. 2026Causal-Audit: A Framework for Risk Assessment of Assumption Violations in Time-Series Causal Discoverycited by 0
  25. 2026Optimization-Free Topological Sort for Causal Discovery via the Schur Complement of Score Jacobianscited by 0
  26. 2026A Topological Sorting Criterion for Random Causal Directed Acyclic Graphscited by 0
  27. 2026Function-Valued Causal Influence in Nonlinear Time Seriescited by 0
  28. 2026CausalArena: Benchmarking Causal Discovery in the Foundation Model Eracited by 0
  29. 2026Hessian Rank Constraint for Learning Structure of Nonlinear Latent Variable Modelscited by 0
  30. 2026Discrete Score Matching Enables Causal Discovery from Count Datacited by 0