mlsanityData to 7 Oct 2026

Causal Discovery with Score Matching on Additive Models with Arbitrary Noise

arXiv 2304.03265 ↗First posted 6 Apr 2023cs.LG stat.MEcited by 41

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Abstract (arXiv)

Causal discovery methods are intrinsically constrained by the set of assumptions needed to ensure structure identifiability. Moreover additional restrictions are often imposed in order to simplify the inference task: this is the case for the Gaussian noise assumption on additive non-linear models, which is common to many causal discovery approaches. In this paper we show the shortcomings of inference under this hypothesis, analyzing the risk of edge inversion under violation of Gaussianity of the noise terms. Then, we propose a novel method for inferring the topological ordering of the variables in the causal graph, from data generated according to an additive non-linear model with a generic noise distribution. This leads to NoGAM (Not only Gaussian Additive noise Models), a causal discovery algorithm with a minimal set of assumptions and state of the art performance, experimentally benchmarked on synthetic data.

Key facts. Cited by 41 papers in the map (data through 7 Oct 2026). Builds on 9 of its 29 references that are in the map. First posted on arXiv 6 Apr 2023.

Builds on

9 of 29 references.

References · 9

  1. 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 745
  2. 2013Causal Discovery with Continuous Additive Noise Modelscited by 252
  3. 2016A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluationcited by 236
  4. 2019Gradient-Based Neural DAG Learningcited by 227
  5. 2013CAM: Causal additive models, high-dimensional order search and penalized regressioncited by 175
  6. 2019Causal Discovery with Reinforcement Learningcited by 145
  7. 2017Measuring Sample Quality with Kernelscited by 119
  8. 2022Score matching enables causal discovery of nonlinear additive noise modelscited by 108
  9. 2017Gradient Estimators for Implicit Modelscited by 58

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 5; 2024: 17; 2025: 9; 2026: 10.

41 papers.

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  1. 2023Assumption violations in causal discovery and the robustness of score matchingcited by 28
  2. 2024Identifiable Exchangeable Mechanisms for Causal Structure and Representation Learningcited by 16
  3. 2023Sample Complexity Bounds for Score-Matching: Causal Discovery and Generative Modelingcited by 15
  4. 2025Estimating Interventional Distributions with Uncertain Causal Graphs through Meta-Learningcited by 11
  5. 2024Demystifying amortized causal discovery with transformerscited by 10
  6. 2024Score matching through the roof: linear, nonlinear, and latent variables causal discoverycited by 8
  7. 2024A Skewness-Based Criterion for Addressing Heteroscedastic Noise in Causal Discoverycited by 7
  8. 2024Identifiability Guarantees for Causal Disentanglement from Purely Observational Datacited by 7
  9. 2024Local Causal Discovery for Structural Evidence of Direct Discriminationcited by 6
  10. 2025Distinguishing Cause from Effect with Causal Velocity Modelscited by 6
  11. 2023iSCAN: Identifying Causal Mechanism Shifts among Nonlinear Additive Noise Modelscited by 5
  12. 2024Hybrid Top-Down Global Causal Discovery with Local Search for Linear and Nonlinear Additive Noise Modelscited by 5
29 more
  1. 2024Deriving Causal Order from Single-Variable Interventions: Guarantees & Algorithmcited by 5
  2. 2024Scalable and Flexible Causal Discovery with an Efficient Test for Adjacencycited by 5
  3. 2024Continuous Bayesian Model Selection for Multivariate Causal Discoverycited by 5
  4. 2023Shortcuts for causal discovery of nonlinear models by score matchingcited by 4
  5. 2024Identifying General Mechanism Shifts in Linear Causal Representationscited by 4
  6. 2026Causal Representation Learning from General Environments under Nonparametric Mixingcited by 4
  7. 2025Causal Discovery via Quantile Partial Effectcited by 3
  8. 2024Efficient Differentiable Discovery of Causal Ordercited by 2
  9. 2026DAG-FM: A Foundation Model for Causal Discovery under Heterogeneous Causal Mechanismscited by 2
  10. 2023Hierarchical Topological Ordering with Conditional Independence Test for Limited Time Seriescited by 1
  11. 2024Causal Layering via Conditional Entropycited by 1
  12. 2024LoSAM: Local Search in Additive Noise Models with Mixed Mechanisms and General Noise for Global Causal Discoverycited by 1
  13. 2024Causal Order Discovery based on Monotonic SCMscited by 1
  14. 2024Score-matching-based Structure Learning for Temporal Data on Networkscited by 1
  15. 2025When Additive Noise Meets Unobserved Mediators: Bivariate Denoising Diffusion for Causal Discoverycited by 1
  16. 2025Causal Discovery for Irregularly Time Series with Consistency Guaranteescited by 1
  17. 2025Causal Ordering for Structure Learning from Time Seriescited by 1
  18. 2026Ordering-based Causal Discovery via Generalized Score Matchingcited by 1
  19. 2026Learning Causal Orderings for In-Context Tabular Predictioncited by 1
  20. 2026Test Time Training for Supervised Causal Learningcited by 1
  21. 2024Unsupervised Pairwise Causal Discovery on Heterogeneous Data using Mutual Information Measurescited by 0
  22. 2025On Theoretical Identifiability of Discrete Latent Causal Graphical Modelscited by 0
  23. 2025Estimating Treatment Effects with Independent Component Analysiscited by 0
  24. 2025On the Identifiability of Causal Graphs with the Invariance Principlecited by 0
  25. 2026Efficient Causal Structure Learning via Modular Subgraph Integrationcited by 0
  26. 2026Root Cause Analysis of Measurement and Mechanistic Anomaliescited by 0
  27. 2026Causal Learning with the Invariance Principlecited by 0
  28. 2026Reconciling Causality and Non-Equilibrium Thermodynamics with Hamiltonian Causal Modelscited by 0
  29. 2026Discrete Score Matching Enables Causal Discovery from Count Datacited by 0