mlsanityData to 14 Oct 2026

DAG-GNN: DAG Structure Learning with Graph Neural Networks

arXiv 1904.10098 ↗First posted 22 Apr 2019cs.LG cs.AI stat.MLcited by 331

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Abstract (arXiv)

Learning a faithful directed acyclic graph (DAG) from samples of a joint distribution is a challenging combinatorial problem, owing to the intractable search space superexponential in the number of graph nodes. A recent breakthrough formulates the problem as a continuous optimization with a structural constraint that ensures acyclicity (Zheng et al., 2018). The authors apply the approach to the linear structural equation model (SEM) and the least-squares loss function that are statistically well justified but nevertheless limited. Motivated by the widespread success of deep learning that is capable of capturing complex nonlinear mappings, in this work we propose a deep generative model and apply a variant of the structural constraint to learn the DAG. At the heart of the generative model is a variational autoencoder parameterized by a novel graph neural network architecture, which we coin DAG-GNN. In addition to the richer capacity, an advantage of the proposed model is that it naturally handles discrete variables as well as vector-valued ones. We demonstrate that on synthetic data sets, the proposed method learns more accurate graphs for nonlinearly generated samples; and on benchmark data sets with discrete variables, the learned graphs are reasonably close to the global optima. The code is available at urlhttps://github.com/fishmoon1234/DAG-GNN.

Key facts. Cited by 331 papers in the map (data through 14 Oct 2026). First posted on arXiv 22 Apr 2019.

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Citing papers per year: 2021: 39; 2022: 58; 2023: 73; 2024: 56; 2025: 49; 2026: 56.

331 papers.

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  1. 2023Causal Reasoning and Large Language Models: Opening a New Frontier for Causalitycited by 353
  2. 2021D'ya like DAGs? A Survey on Structure Learning and Causal Discoverycited by 211
  3. 2021Discrete Graph Structure Learning for Forecasting Multiple Time Seriescited by 171
  4. 2021Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Gamecited by 161
  5. 2022DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterizationcited by 140
  6. 2022Deep Learning for Time Series Anomaly Detection: A Surveycited by 131
  7. 2022Disentangled Representation Learningcited by 112
  8. 2021DiBS: Differentiable Bayesian Structure Learningcited by 106
  9. 2023Learning Linear Causal Representations from Interventions under General Nonlinear Mixingcited by 92
  10. 2022Amortized Inference for Causal Structure Learningcited by 90
  11. 2021Parameter Prediction for Unseen Deep Architecturescited by 89
  12. 2021Efficient Neural Causal Discovery without Acyclicity Constraintscited by 82
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  1. 2021BCD Nets: Scalable Variational Approaches for Bayesian Causal Discoverycited by 68
  2. 2022Learning to Induce Causal Structurecited by 68
  3. 2022Diffusion Models for Causal Discovery via Topological Orderingcited by 66
  4. 2021gCastle: A Python Toolbox for Causal Discoverycited by 61
  5. 2021Ordering-Based Causal Discovery with Reinforcement Learningcited by 55
  6. 2021DAGs with No Curl: An Efficient DAG Structure Learning Approachcited by 53
  7. 2021Unsuitability of NOTEARS for Causal Graph Discoverycited by 47
  8. 2022Differentiable DAG Samplingcited by 47
  9. 2022Large-Scale Differentiable Causal Discovery of Factor Graphscited by 47
  10. 2022Causal Structure Learning: a Combinatorial Perspectivecited by 46
  11. 2021Variational Causal Networks: Approximate Bayesian Inference over Causal Structurescited by 43
  12. 2023Causal Discovery from Temporal Data: An Overview and New Perspectivescited by 43
  13. 2022Graph-Augmented Normalizing Flows for Anomaly Detection of Multiple Time Seriescited by 42
  14. 2021Learning Neural Causal Models with Active Interventionscited by 40
  15. 2023Structure Learning with Continuous Optimization: A Sober Look and Beyondcited by 36
  16. 2023A Survey on Causal Discovery Methods for I.I.D. and Time Series Datacited by 35
  17. 2022Identifying Weight-Variant Latent Causal Modelscited by 34
  18. 2023BayesDAG: Gradient-Based Posterior Inference for Causal Discoverycited by 33
  19. 2024Causal Inference with Large Language Model: A Surveycited by 32
  20. 2021Towards Federated Bayesian Network Structure Learning with Continuous Optimizationcited by 31
  21. 2023Stable Differentiable Causal Discoverycited by 31
  22. 2022Bayesian learning of Causal Structure and Mechanisms with GFlowNets and Variational Bayescited by 30
  23. 2024How Realistic Is Your Synthetic Data? Constraining Deep Generative Models for Tabular Datacited by 29
  24. 2022BaCaDI: Bayesian Causal Discovery with Unknown Interventionscited by 26
  25. 2021Simultaneously Reconciled Quantile Forecasting of Hierarchically Related Time Seriescited by 24
  26. 2022Truncated Matrix Power Iteration for Differentiable DAG Learningcited by 23
  27. 2021Data Generating Process to Evaluate Causal Discovery Techniques for Time Series Datacited by 22
  28. 2022MissDAG: Causal Discovery in the Presence of Missing Data with Continuous Additive Noise Modelscited by 22
  29. 2023From Identifiable Causal Representations to Controllable Counterfactual Generation: A Survey on Causal Generative Modelingcited by 22
  30. 2023NODAGS-Flow: Nonlinear Cyclic Causal Structure Learningcited by 20
  31. 2021VACA: Design of Variational Graph Autoencoders for Interventional and Counterfactual Queriescited by 19
  32. 2023Automated Scientific Discovery: From Equation Discovery to Autonomous Discovery Systemscited by 19
  33. 2024Signature Kernel Conditional Independence Tests in Causal Discovery for Stochastic Processescited by 18
  34. 2021A data-driven peridynamic continuum model for upscaling molecular dynamicscited by 17
  35. 2021FedDAG: Federated DAG Structure Learningcited by 17
  36. 2023Optimizing NOTEARS Objectives via Topological Swapscited by 17
  37. 2024Standardizing Structural Causal Modelscited by 17
  38. 2021Simultaneous Missing Value Imputation and Structure Learning with Groupscited by 16

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