mlsanityData to 14 Oct 2026

Truncated Matrix Power Iteration for Differentiable DAG Learning

arXiv 2208.14571 ↗First posted 30 Aug 2022cs.LG cs.AI stat.MLcited by 23

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Abstract (arXiv)

Recovering underlying Directed Acyclic Graph (DAG) structures from observational data is highly challenging due to the combinatorial nature of the DAG-constrained optimization problem. Recently, DAG learning has been cast as a continuous optimization problem by characterizing the DAG constraint as a smooth equality one, generally based on polynomials over adjacency matrices. Existing methods place very small coefficients on high-order polynomial terms for stabilization, since they argue that large coefficients on the higher-order terms are harmful due to numeric exploding. On the contrary, we discover that large coefficients on higher-order terms are beneficial for DAG learning, when the spectral radiuses of the adjacency matrices are small, and that larger coefficients for higher-order terms can approximate the DAG constraints much better than the small counterparts. Based on this, we propose a novel DAG learning method with efficient truncated matrix power iteration to approximate geometric series based DAG constraints. Empirically, our DAG learning method outperforms the previous state-of-the-arts in various settings, often by a factor of 3 or more in terms of structural Hamming distance.

Key facts. Cited by 23 papers in the map (data through 14 Oct 2026). Builds on 18 of its 57 references that are in the map. First posted on arXiv 30 Aug 2022.

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18 of 57 references.

References · 18

  1. 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 752
  2. 2019DAG-GNN: DAG Structure Learning with Graph Neural Networkscited by 331
  3. 2019Gradient-Based Neural DAG Learningcited by 227
  4. 2021D'ya like DAGs? A Survey on Structure Learning and Causal Discoverycited by 211
  5. 2019Learning Sparse Nonparametric DAGscited by 207
  6. 2020DYNOTEARS: Structure Learning from Time-Series Datacited by 200
  7. 2020On the Role of Sparsity and DAG Constraints for Learning Linear DAGscited by 191
  8. 2013Causal Inference in the Presence of Latent Variables and Selection Biascited by 166
  9. 2019Causal Discovery with Reinforcement Learningcited by 145
  10. 2019Masked Gradient-Based Causal Structure Learningcited by 89
  11. 2013High-dimensional learning of linear causal networks via inverse covariance estimationcited by 87
  12. 2020DAGs with No Fears: A Closer Look at Continuous Optimization for Learning Bayesian Networkscited by 66
6 more
  1. 2020Differentiable Causal Discovery Under Unmeasured Confoundingcited by 56
  2. 2021DAGs with No Curl: An Efficient DAG Structure Learning Approachcited by 53
  3. 2019Causal Discovery Toolbox: Uncover causal relationships in Pythoncited by 49
  4. 2019Scaling structural learning with NO-BEARS to infer causal transcriptome networkscited by 39
  5. 2020On the Convergence of Continuous Constrained Optimization for Structure Learningcited by 38
  6. 2020Efficient and Scalable Structure Learning for Bayesian Networks: Algorithms and Applicationscited by 11

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Citing papers per year: 2022: 2; 2023: 6; 2024: 8; 2025: 5; 2026: 2.

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  1. 2023Structure Learning with Continuous Optimization: A Sober Look and Beyondcited by 36
  2. 2023textttcausalAssembly: Generating Realistic Production Data for Benchmarking Causal Discoverycited by 18
  3. 2024Demystifying amortized causal discovery with transformerscited by 11
  4. 2023Constraint-Free Structure Learning with Smooth Acyclic Orientationscited by 10
  5. 2023Industrial Internet of Things Intelligence Empowering Smart Manufacturing: A Literature Reviewcited by 8
  6. 2024Markov Equivalence and Consistency in Differentiable Structure Learningcited by 7
  7. 2022Learning Latent Structural Causal Modelscited by 5
  8. 2024On the Identifiability of Sparse ICA without Assuming Non-Gaussianitycited by 5
  9. 2025Analytic DAG Constraints for Differentiable DAG Learningcited by 5
  10. 2024psiDAG: Projected Stochastic Approximation Iteration for DAG Structure Learningcited by 4
  11. 2025Learning Causal Graphs at Scale: A Foundation Model Approachcited by 4
  12. 2022On the Sparse DAG Structure Learning Based on Adaptive Lassocited by 3
11 more
  1. 2023Granger Causal Inference in Multivariate Hawkes Processes by Minimum Message Lengthcited by 3
  2. 2024Reinforcement Learning for Causal Discovery without Acyclicity Constraintscited by 3
  3. 2025Score-based Greedy Search for Structure Identification of Partially Observed Linear Causal Modelscited by 2
  4. 2023Causal Graph Discovery from Self and Mutually Exciting Time Seriescited by 1
  5. 2024Scalable Variational Causal Discovery Unconstrained by Acyclicitycited by 1
  6. 2024Revisiting Differentiable Structure Learning: Inconsistency of ℓ1 Penalty and Beyondcited by 1
  7. 2024Fast Causal Discovery by Approximate Kernel-based Generalized Score Functions with Linear Computational Complexitycited by 1
  8. 2025Causal Discovery via Bayesian Optimizationcited by 1
  9. 2025Differentiable Structure Learning and Causal Discovery for General Binary Datacited by 0
  10. 2026Efficient Differentiable Causal Discovery via Reliable Super-Structure Learningcited by 0
  11. 2026Structure Learning on Clustered Datacited by 0