mlsanityData to 14 Oct 2026

Masked Gradient-Based Causal Structure Learning

arXiv 1910.08527 ↗First posted 18 Oct 2019cs.LG stat.ME stat.MLcited by 89

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Abstract (arXiv)

This paper studies the problem of learning causal structures from observational data. We reformulate the Structural Equation Model (SEM) with additive noises in a form parameterized by binary graph adjacency matrix and show that, if the original SEM is identifiable, then the binary adjacency matrix can be identified up to super-graphs of the true causal graph under mild conditions. We then utilize the reformulated SEM to develop a causal structure learning method that can be efficiently trained using gradient-based optimization, by leveraging a smooth characterization on acyclicity and the Gumbel-Softmax approach to approximate the binary adjacency matrix. It is found that the obtained entries are typically near zero or one and can be easily thresholded to identify the edges. We conduct experiments on synthetic and real datasets to validate the effectiveness of the proposed method, and show that it readily includes different smooth model functions and achieves a much improved performance on most datasets considered.

Key facts. Cited by 89 papers in the map (data through 14 Oct 2026). First posted on arXiv 18 Oct 2019.

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Citing papers per year: 2021: 12; 2022: 19; 2023: 19; 2024: 18; 2025: 13; 2026: 8.

89 papers.

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  1. 2021D'ya like DAGs? A Survey on Structure Learning and Causal Discoverycited by 211
  2. 2021Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICAcited by 160
  3. 2021DiBS: Differentiable Bayesian Structure Learningcited by 106
  4. 2022Diffusion Models for Causal Discovery via Topological Orderingcited by 66
  5. 2021gCastle: A Python Toolbox for Causal Discoverycited by 61
  6. 2021Ordering-Based Causal Discovery with Reinforcement Learningcited by 55
  7. 2021DAGs with No Curl: An Efficient DAG Structure Learning Approachcited by 53
  8. 2022Causal Representation Learning for Instantaneous and Temporal Effects in Interactive Systemscited by 51
  9. 2021Unsuitability of NOTEARS for Causal Graph Discoverycited by 47
  10. 2022Differentiable DAG Samplingcited by 47
  11. 2022Large-Scale Differentiable Causal Discovery of Factor Graphscited by 47
  12. 2023Causal Discovery from Temporal Data: An Overview and New Perspectivescited by 43
38 more
  1. 2023Structure Learning with Continuous Optimization: A Sober Look and Beyondcited by 36
  2. 2023A Survey on Causal Discovery Methods for I.I.D. and Time Series Datacited by 35
  3. 2021Towards Federated Bayesian Network Structure Learning with Continuous Optimizationcited by 31
  4. 2022Improving Multi-Task Generalization via Regularizing Spurious Correlationcited by 28
  5. 2022Truncated Matrix Power Iteration for Differentiable DAG Learningcited by 23
  6. 2022MissDAG: Causal Discovery in the Presence of Missing Data with Continuous Additive Noise Modelscited by 22
  7. 2023From Identifiable Causal Representations to Controllable Counterfactual Generation: A Survey on Causal Generative Modelingcited by 22
  8. 2022Differentiable Causal Discovery Under Latent Interventionscited by 21
  9. 2023NODAGS-Flow: Nonlinear Cyclic Causal Structure Learningcited by 20
  10. 2021FedDAG: Federated DAG Structure Learningcited by 17
  11. 2024DeepRicci: Self-supervised Graph Structure-Feature Co-Refinement for Alleviating Over-squashingcited by 16
  12. 2024Identifiable Exchangeable Mechanisms for Causal Structure and Representation Learningcited by 16
  13. 2023Learning Causally Disentangled Representations via the Principle of Independent Causal Mechanismscited by 14
  14. 2023RDGSL: Dynamic Graph Representation Learning with Structure Learningcited by 13
  15. 2024RealTCD: Temporal Causal Discovery from Interventional Data with Large Language Modelcited by 13
  16. 2022Guided Hybrid Quantization for Object detection in Multimodal Remote Sensing Imagery via One-to-one Self-teachingcited by 12
  17. 2021ML4C: Seeing Causality Through Latent Vicinitycited by 11
  18. 2022Towards Privacy-Aware Causal Structure Learning in Federated Settingcited by 11
  19. 2023Federated Causality Learning with Explainable Adaptive Optimizationcited by 11
  20. 2021Multi-task Learning of Order-Consistent Causal Graphscited by 10
  21. 2022CIPCaD-Bench: Continuous Industrial Process datasets for benchmarking Causal Discovery methodscited by 10
  22. 2022Novel Ordering-based Approaches for Causal Structure Learning in the Presence of Unobserved Variablescited by 10
  23. 2023Emerging Synergies in Causality and Deep Generative Models: A Surveycited by 10
  24. 2023Constraint-Free Structure Learning with Smooth Acyclic Orientationscited by 10
  25. 2023Effective Causal Discovery under Identifiable Heteroscedastic Noise Modelcited by 10
  26. 2023Evaluation of Induced Expert Knowledge in Causal Structure Learning by NOTEARScited by 8
  27. 2023Open problems in causal structure learning: A case study of COVID-19 in the UKcited by 7
  28. 2025Learning General Causal Structures with Hidden Dynamic Process for Climate Analysiscited by 7
  29. 2023MetaPhysiCa: OOD Robustness in Physics-informed Machine Learningcited by 6
  30. 2024Optimal Transport for Structure Learning Under Missing Datacited by 6
  31. 2025Rethinking Spatio-Temporal Anomaly Detection: A Vision for Causality-Driven Cybersecuritycited by 6
  32. 2021On the Role of Entropy-based Loss for Learning Causal Structures with Continuous Optimizationcited by 5
  33. 2022Learning Latent Structural Causal Modelscited by 5
  34. 2023Boosting Differentiable Causal Discovery via Adaptive Sample Reweightingcited by 5
  35. 2024Causal Representation Learning in Temporal Data via Single-Parent Decodingcited by 5
  36. 2024On Discovery of Local Independence over Continuous Variables via Neural Contextual Decompositioncited by 4
  37. 2024psiDAG: Projected Stochastic Approximation Iteration for DAG Structure Learningcited by 4
  38. 2025Differentiable Cyclic Causal Discovery Under Unmeasured Confounderscited by 4

50 most cited of 89 All 89 (JSON)