mlsanityData to 7 Oct 2026

On the Role of Sparsity and DAG Constraints for Learning Linear DAGs

arXiv 2006.10201 ↗First posted 17 Jun 2020cs.LG stat.MLcited by 186

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Abstract (arXiv)

Learning graphical structures based on Directed Acyclic Graphs (DAGs) is a challenging problem, partly owing to the large search space of possible graphs. A recent line of work formulates the structure learning problem as a continuous constrained optimization task using the least squares objective and an algebraic characterization of DAGs. However, the formulation requires a hard DAG constraint and may lead to optimization difficulties. In this paper, we study the asymptotic role of the sparsity and DAG constraints for learning DAG models in the linear Gaussian and non-Gaussian cases, and investigate their usefulness in the finite sample regime. Based on the theoretical results, we formulate a likelihood-based score function, and show that one only has to apply soft sparsity and DAG constraints to learn a DAG equivalent to the ground truth DAG. This leads to an unconstrained optimization problem that is much easier to solve. Using gradient-based optimization and GPU acceleration, our procedure can easily handle thousands of nodes while retaining a high accuracy. Extensive experiments validate the effectiveness of our proposed method and show that the DAG-penalized likelihood objective is indeed favorable over the least squares one with the hard DAG constraint.

Key facts. Cited by 186 papers in the map (data through 7 Oct 2026). First posted on arXiv 17 Jun 2020.

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Citing papers per year: 2021: 18; 2022: 29; 2023: 38; 2024: 29; 2025: 33; 2026: 39.

186 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. 2022Deep End-to-end Causal Inferencecited by 93
  6. 2021Efficient Neural Causal Discovery without Acyclicity Constraintscited by 82
  7. 2021BCD Nets: Scalable Variational Approaches for Bayesian Causal Discoverycited by 68
  8. 2021gCastle: A Python Toolbox for Causal Discoverycited by 60
  9. 2021DAGs with No Curl: An Efficient DAG Structure Learning Approachcited by 53
  10. 2022Large-Scale Differentiable Causal Discovery of Factor Graphscited by 47
  11. 2021Unsuitability of NOTEARS for Causal Graph Discoverycited by 46
  12. 2023Fast Scalable and Accurate Discovery of DAGs Using the Best Order Score Search and Grow-Shrink Treescited by 38
38 more
  1. 2023A Survey on Causal Discovery Methods for I.I.D. and Time Series Datacited by 35
  2. 2023Structure Learning with Continuous Optimization: A Sober Look and Beyondcited by 34
  3. 2021NTS-NOTEARS: Learning Nonparametric DBNs With Prior Knowledgecited by 33
  4. 2023Discovering Causal Relations and Equations from Datacited by 33
  5. 2021Towards Federated Bayesian Network Structure Learning with Continuous Optimizationcited by 31
  6. 2023Causal Representation Learning Made Identifiable by Grouping of Observational Variablescited by 30
  7. 2023Stable Differentiable Causal Discoverycited by 30
  8. 2022Truncated Matrix Power Iteration for Differentiable DAG Learningcited by 23
  9. 2021Data Generating Process to Evaluate Causal Discovery Techniques for Time Series Datacited by 22
  10. 2023Self-Compatibility: Evaluating Causal Discovery without Ground Truthcited by 22
  11. 2022MissDAG: Causal Discovery in the Presence of Missing Data with Continuous Additive Noise Modelscited by 21
  12. 2023NODAGS-Flow: Nonlinear Cyclic Causal Structure Learningcited by 20
  13. 2022Reliable Causal Discovery with Improved Exact Search and Weaker Assumptionscited by 19
  14. 2023Hierarchical Graph Neural Networks for Causal Discovery and Root Cause Localizationcited by 18
  15. 2023textttcausalAssembly: Generating Realistic Production Data for Benchmarking Causal Discoverycited by 18
  16. 2021FedDAG: Federated DAG Structure Learningcited by 17
  17. 2022CausPref: Causal Preference Learning for Out-of-Distribution Recommendationcited by 17
  18. 2023Optimizing NOTEARS Objectives via Topological Swapscited by 17
  19. 2024Standardizing Structural Causal Modelscited by 17
  20. 2021Simultaneous Missing Value Imputation and Structure Learning with Groupscited by 16
  21. 2023MM-DAG: Multi-task DAG Learning for Multi-modal Data -- with Application for Traffic Congestion Analysiscited by 13
  22. 2022Causal Fourier Analysis on Directed Acyclic Graphs and Posetscited by 12
  23. 2022Learning Task-Aware Effective Brain Connectivity for fMRI Analysis with Graph Neural Networkscited by 12
  24. 2022Characterization and Greedy Learning of Gaussian Structural Causal Models under Unknown Interventionscited by 12
  25. 2023CoLiDE: Concomitant Linear DAG Estimationcited by 12
  26. 2022GFlowCausal: Generative Flow Networks for Causal Discoverycited by 11
  27. 2022Towards Privacy-Aware Causal Structure Learning in Federated Settingcited by 11
  28. 2024Ordering-Based Causal Discovery for Linear and Nonlinear Relationscited by 11
  29. 2022CIPCaD-Bench: Continuous Industrial Process datasets for benchmarking Causal Discovery methodscited by 10
  30. 2022Sparsity in Continuous-Depth Neural Networkscited by 10
  31. 2023Global Optimality in Bivariate Gradient-based DAG Learningcited by 10
  32. 2023Constraint-Free Structure Learning with Smooth Acyclic Orientationscited by 10
  33. 2024Demystifying amortized causal discovery with transformerscited by 10
  34. 2021Deconfounded Score Method: Scoring DAGs with Dense Unobserved Confoundingcited by 9
  35. 2023DAG Learning on the Permutahedroncited by 9
  36. 2024LEMMA-RCA: A Large Multi-modal Multi-domain Dataset for Root Cause Analysiscited by 9
  37. 2023Evaluation of Induced Expert Knowledge in Causal Structure Learning by NOTEARScited by 8
  38. 2023Learning DAGs from Data with Few Root Causescited by 8

50 most cited of 186 All 186 (JSON)