mlsanityData to 7 Oct 2026

Learning Sparse Nonparametric DAGs

arXiv 1909.13189 ↗First posted 29 Sep 2019stat.ML cs.LG stat.MEcited by 207

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Abstract (arXiv)

We develop a framework for learning sparse nonparametric directed acyclic graphs (DAGs) from data. Our approach is based on a recent algebraic characterization of DAGs that led to a fully continuous program for score-based learning of DAG models parametrized by a linear structural equation model (SEM). We extend this algebraic characterization to nonparametric SEM by leveraging nonparametric sparsity based on partial derivatives, resulting in a continuous optimization problem that can be applied to a variety of nonparametric and semiparametric models including GLMs, additive noise models, and index models as special cases. Unlike existing approaches that require specific modeling choices, loss functions, or algorithms, we present a completely general framework that can be applied to general nonlinear models (e.g. without additive noise), general differentiable loss functions, and generic black-box optimization routines. The code is available at https://github.com/xunzheng/notears.

Key facts. Cited by 207 papers in the map (data through 7 Oct 2026). First posted on arXiv 29 Sep 2019.

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Citing papers per year: 2021: 30; 2022: 38; 2023: 46; 2024: 30; 2025: 27; 2026: 36.

207 papers.

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  1. 2021D'ya like DAGs? A Survey on Structure Learning and Causal Discoverycited by 209
  2. 2021Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Gamecited by 159
  3. 2022DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterizationcited by 135
  4. 2021DiBS: Differentiable Bayesian Structure Learningcited by 105
  5. 2023Nonparametric Identifiability of Causal Representations from Unknown Interventionscited by 105
  6. 2022Deep End-to-end Causal Inferencecited by 93
  7. 2021Efficient Neural Causal Discovery without Acyclicity Constraintscited by 82
  8. 2022Diffusion Models for Causal Discovery via Topological Orderingcited by 64
  9. 2021gCastle: A Python Toolbox for Causal Discoverycited by 60
  10. 2021Ordering-Based Causal Discovery with Reinforcement Learningcited by 55
  11. 2021DAGs with No Curl: An Efficient DAG Structure Learning Approachcited by 53
  12. 2021MIRACLE: Causally-Aware Imputation via Learning Missing Data Mechanismscited by 50
38 more
  1. 2022Large-Scale Differentiable Causal Discovery of Factor Graphscited by 47
  2. 2021Unsuitability of NOTEARS for Causal Graph Discoverycited by 46
  3. 2023Causal Discovery from Temporal Data: An Overview and New Perspectivescited by 43
  4. 2021Learning Neural Causal Models with Active Interventionscited by 40
  5. 2023Structure Learning with Continuous Optimization: A Sober Look and Beyondcited by 34
  6. 2021NTS-NOTEARS: Learning Nonparametric DBNs With Prior Knowledgecited by 33
  7. 2022Identifying Weight-Variant Latent Causal Modelscited by 33
  8. 2023Discovering Causal Relations and Equations from Datacited by 33
  9. 2022Distributed Graph Neural Network Training: A Surveycited by 32
  10. 2021Towards Federated Bayesian Network Structure Learning with Continuous Optimizationcited by 31
  11. 2021ACRE: Abstract Causal REasoning Beyond Covariationcited by 30
  12. 2023Causal Representation Learning Made Identifiable by Grouping of Observational Variablescited by 30
  13. 2023Stable Differentiable Causal Discoverycited by 30
  14. 2022CausalBench: A Large-scale Benchmark for Network Inference from Single-cell Perturbation Datacited by 29
  15. 2023Assumption violations in causal discovery and the robustness of score matchingcited by 28
  16. 2022BaCaDI: Bayesian Causal Discovery with Unknown Interventionscited by 26
  17. 2022Truncated Matrix Power Iteration for Differentiable DAG Learningcited by 23
  18. 2021Data Generating Process to Evaluate Causal Discovery Techniques for Time Series Datacited by 22
  19. 2023Self-Compatibility: Evaluating Causal Discovery without Ground Truthcited by 22
  20. 2022Differentiable Causal Discovery Under Latent Interventionscited by 21
  21. 2022MissDAG: Causal Discovery in the Presence of Missing Data with Continuous Additive Noise Modelscited by 21
  22. 2023NODAGS-Flow: Nonlinear Cyclic Causal Structure Learningcited by 20
  23. 2023Causal Deep Learningcited by 20
  24. 2021A Theoretical Analysis on Independence-driven Importance Weighting for Covariate-shift Generalizationcited by 18
  25. 2023Automated Scientific Discovery: From Equation Discovery to Autonomous Discovery Systemscited by 18
  26. 2023textttcausalAssembly: Generating Realistic Production Data for Benchmarking Causal Discoverycited by 18
  27. 2024Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processescited by 18
  28. 2021FedDAG: Federated DAG Structure Learningcited by 17
  29. 2022CausPref: Causal Preference Learning for Out-of-Distribution Recommendationcited by 17
  30. 2023Optimizing NOTEARS Objectives via Topological Swapscited by 17
  31. 2024Standardizing Structural Causal Modelscited by 17
  32. 2021Simultaneous Missing Value Imputation and Structure Learning with Groupscited by 16
  33. 2023Causal Reasoning in the Presence of Latent Confounders via Neural ADMG Learningcited by 15
  34. 2021Efficient Bayesian network structure learning via local Markov boundary searchcited by 14
  35. 2023On Learning Necessary and Sufficient Causal Graphscited by 14
  36. 2023Computably Continuous Reinforcement-Learning Objectives are PAC-learnablecited by 13
  37. 2023MM-DAG: Multi-task DAG Learning for Multi-modal Data -- with Application for Traffic Congestion Analysiscited by 13
  38. 2022Characterization and Greedy Learning of Gaussian Structural Causal Models under Unknown Interventionscited by 12

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