mlsanityData to 7 Oct 2026

DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterization

arXiv 2209.08037 ↗First posted 16 Sep 2022cs.LG stat.ME stat.MLcited by 135

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Abstract (arXiv)

The combinatorial problem of learning directed acyclic graphs (DAGs) from data was recently framed as a purely continuous optimization problem by leveraging a differentiable acyclicity characterization of DAGs based on the trace of a matrix exponential function. Existing acyclicity characterizations are based on the idea that powers of an adjacency matrix contain information about walks and cycles. In this work, we propose a new acyclicity characterization based on the log-determinant (log-det) function, which leverages the nilpotency property of DAGs. To deal with the inherent asymmetries of a DAG, we relate the domain of our log-det characterization to the set of textitM-matrices, which is a key difference to the classical log-det function defined over the cone of positive definite matrices. Similar to acyclicity functions previously proposed, our characterization is also exact and differentiable. However, when compared to existing characterizations, our log-det function: (1) Is better at detecting large cycles; (2) Has better-behaved gradients; and (3) Its runtime is in practice about an order of magnitude faster. From the optimization side, we drop the typically used augmented Lagrangian scheme and propose DAGMA (textitDAGs via M-matrices for Acyclicity), a method that resembles the central path for barrier methods. Each point in the central path of DAGMA is a solution to an unconstrained problem regularized by our log-det function, then we show that at the limit of the central path the solution is guaranteed to be a DAG. Finally, we provide extensive experiments for textitlinear and textitnonlinear SEMs and show that our approach can reach large speed-ups and smaller structural Hamming distances against state-of-the-art methods. Code implementing the proposed method is open-source and publicly available at https://github.com/kevinsbello/dagma.

Key facts. Cited by 135 papers in the map (data through 7 Oct 2026). Builds on 27 of its 72 references that are in the map. First posted on arXiv 16 Sep 2022.

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27 of 72 references.

References · 27

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2021Convex optimizationcited by 2,479
  3. 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 745
  4. 2019DAG-GNN: DAG Structure Learning with Graph Neural Networkscited by 329
  5. 2013Causal Discovery with Continuous Additive Noise Modelscited by 252
  6. 2019Gradient-Based Neural DAG Learningcited by 227
  7. 2019Learning Sparse Nonparametric DAGscited by 207
  8. 2020DYNOTEARS: Structure Learning from Time-Series Datacited by 198
  9. 2020On the Role of Sparsity and DAG Constraints for Learning Linear DAGscited by 186
  10. 2013Learning Bayesian Networks: The Combination of Knowledge and Statistical Datacited by 185
  11. 2013CAM: Causal additive models, high-dimensional order search and penalized regressioncited by 175
  12. 2019Causal Discovery with Reinforcement Learningcited by 145
15 more
  1. 2013High-dimensional learning of linear causal networks via inverse covariance estimationcited by 86
  2. 2020DAGs with No Fears: A Closer Look at Continuous Optimization for Learning Bayesian Networkscited by 66
  3. 2019Causal Discovery with General Non-Linear Relationships Using Non-Linear ICAcited by 58
  4. 2020Differentiable Causal Discovery Under Unmeasured Confoundingcited by 56
  5. 2021DAGs with No Curl: An Efficient DAG Structure Learning Approachcited by 53
  6. 2017Learning linear structural equation models in polynomial time and sample complexitycited by 49
  7. 2020CASTLE: Regularization via Auxiliary Causal Graph Discoverycited by 41
  8. 2020On the Convergence of Continuous Constrained Optimization for Structure Learningcited by 38
  9. 2014Concave Penalized Estimation of Sparse Gaussian Bayesian Networkscited by 27
  10. 2017Learning Identifiable Gaussian Bayesian Networks in Polynomial Time and Sample Complexitycited by 27
  11. 2017Learning Quadratic Variance Function (QVF) DAG models via OverDispersion Scoring (ODS)cited by 18
  12. 2020Causal Adversarial Network for Learning Conditional and Interventional Distributionscited by 13
  13. 2014Penalized Estimation of Directed Acyclic Graphs From Discrete Datacited by 10
  14. 2018High-Dimensional Poisson DAG Model Learning Using ℓ1-Regularized Regressioncited by 10
  15. 2013Graph estimation with joint additive modelscited by 6

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Citing papers per year: 2023: 21; 2024: 30; 2025: 34; 2026: 50.

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  1. 2023Learning Linear Causal Representations from Interventions under General Nonlinear Mixingcited by 92
  2. 2023Fast Scalable and Accurate Discovery of DAGs Using the Best Order Score Search and Grow-Shrink Treescited by 38
  3. 2023Structure Learning with Continuous Optimization: A Sober Look and Beyondcited by 34
  4. 2023Discovering Causal Relations and Equations from Datacited by 33
  5. 2023Stable Differentiable Causal Discoverycited by 30
  6. 2023Reimagining Synthetic Tabular Data Generation through Data-Centric AI: A Comprehensive Benchmarkcited by 23
  7. 2023Optimizing NOTEARS Objectives via Topological Swapscited by 17
  8. 2024ACE : Off-Policy Actor-Critic with Causality-Aware Entropy Regularizationcited by 16
  9. 2023CoLiDE: Concomitant Linear DAG Estimationcited by 12
  10. 2024Ordering-Based Causal Discovery for Linear and Nonlinear Relationscited by 11
  11. 2023Global Optimality in Bivariate Gradient-based DAG Learningcited by 10
  12. 2023Constraint-Free Structure Learning with Smooth Acyclic Orientationscited by 10
38 more
  1. 2024Demystifying amortized causal discovery with transformerscited by 10
  2. 2023DAG Learning on the Permutahedroncited by 9
  3. 2023Learning DAGs from Data with Few Root Causescited by 8
  4. 2024DCILP: A Distributed Approach for Large-Scale Causal Structure Learningcited by 8
  5. 2024C2P: Featuring Large Language Models with Causal Reasoningcited by 8
  6. 2024Non-negative Weighted DAG Structure Learningcited by 7
  7. 2024A Skewness-Based Criterion for Addressing Heteroscedastic Noise in Causal Discoverycited by 7
  8. 2023Predictive Coding beyond Correlationscited by 6
  9. 2024Dagma-DCE: Interpretable, Non-Parametric Differentiable Causal Discoverycited by 6
  10. 2024Better Simulations for Validating Causal Discovery with the DAG-Adaptation of the Onion Methodcited by 6
  11. 2024Markov Equivalence and Consistency in Differentiable Structure Learningcited by 6
  12. 2024LLM-initialized Differentiable Causal Discoverycited by 6
  13. 2023Boosting Differentiable Causal Discovery via Adaptive Sample Reweightingcited by 5
  14. 2023iSCAN: Identifying Causal Mechanism Shifts among Nonlinear Additive Noise Modelscited by 5
  15. 2024Optimal Transport for Structure Learning Under Missing Datacited by 5
  16. 2024Scalable and Flexible Causal Discovery with an Efficient Test for Adjacencycited by 5
  17. 2024Continuous Bayesian Model Selection for Multivariate Causal Discoverycited by 5
  18. 2025Fairness-Driven LLM-based Causal Discovery with Active Learning and Dynamic Scoringcited by 5
  19. 2025Analytic DAG Constraints for Differentiable DAG Learningcited by 5
  20. 2024Permutation-based Inference for Variational Learning of Directed Acyclic Graphscited by 4
  21. 2024ProDAG: Projected Variational Inference for Directed Acyclic Graphscited by 4
  22. 2024Causal Discovery over High-Dimensional Structured Hypothesis Spaces with Causal Graph Partitioningcited by 4
  23. 2024Visual Analysis of Multi-outcome Causal Graphscited by 4
  24. 2025Since Faithfulness Fails: The Performance Limits of Neural Causal Discoverycited by 4
  25. 2025Learning Causal Graphs at Scale: A Foundation Model Approachcited by 4
  26. 2025Differentiable Cyclic Causal Discovery Under Unmeasured Confounderscited by 4
  27. 2025Causal-Adapter: Taming Text-to-Image Diffusion for Faithful Counterfactual Generationcited by 4
  28. 2025Embracing Discrete Search: A Reasonable Approach to Causal Structure Learningcited by 4
  29. 2025The Robustness of Differentiable Causal Discovery in Misspecified Scenarioscited by 4
  30. 2025Differentiable Constraint-Based Causal Discoverycited by 4
  31. 2025BUILD with Precision: Bottom-Up Inference of Linear DAGscited by 4
  32. 2026Arrow: A Foundation Model for Causal Discoverycited by 4
  33. 2024Reinforcement Learning for Causal Discovery without Acyclicity Constraintscited by 3
  34. 2024psiDAG: Projected Stochastic Approximation Iteration for DAG Structure Learningcited by 3
  35. 2025ACCESS : A Benchmark for Abstract Causal Event Discovery and Reasoningcited by 3
  36. 2025Causal Discovery via Quantile Partial Effectcited by 3
  37. 2026Exploiting Non-Negativity in DAG Structure Learningcited by 3
  38. 2026FoundCause: Causal Discovery with Latent Confounders from Observational Datacited by 3

50 most cited of 135 All 135 (JSON)