mlsanityData to 14 Oct 2026

Constraint-Free Structure Learning with Smooth Acyclic Orientations

arXiv 2309.08406 ↗First posted 15 Sep 2023cs.LG stat.MLcited by 10

Not on the map. Why?

Abstract (arXiv)

The structure learning problem consists of fitting data generated by a Directed Acyclic Graph (DAG) to correctly reconstruct its arcs. In this context, differentiable approaches constrain or regularize the optimization problem using a continuous relaxation of the acyclicity property. The computational cost of evaluating graph acyclicity is cubic on the number of nodes and significantly affects scalability. In this paper we introduce COSMO, a constraint-free continuous optimization scheme for acyclic structure learning. At the core of our method, we define a differentiable approximation of an orientation matrix parameterized by a single priority vector. Differently from previous work, our parameterization fits a smooth orientation matrix and the resulting acyclic adjacency matrix without evaluating acyclicity at any step. Despite the absence of explicit constraints, we prove that COSMO always converges to an acyclic solution. In addition to being asymptotically faster, our empirical analysis highlights how COSMO performance on graph reconstruction compares favorably with competing structure learning methods.

Key facts. Cited by 10 papers in the map (data through 14 Oct 2026). Builds on 31 of its 45 references that are in the map. First posted on arXiv 15 Sep 2023.

Builds on

31 of 45 references.

References · 31

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 752
  3. 2019Gradient-Based Neural DAG Learningcited by 227
  4. 2020Differentiable Causal Discovery from Interventional Datacited by 218
  5. 2021D'ya like DAGs? A Survey on Structure Learning and Causal Discoverycited by 211
  6. 2019Learning Sparse Nonparametric DAGscited by 207
  7. 2020On the Role of Sparsity and DAG Constraints for Learning Linear DAGscited by 191
  8. 2021Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Gamecited by 161
  9. 2022DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterizationcited by 140
  10. 2022Amortized Inference for Causal Structure Learningcited by 90
  11. 2019Masked Gradient-Based Causal Structure Learningcited by 89
  12. 2013High-dimensional learning of linear causal networks via inverse covariance estimationcited by 87
19 more
  1. 2017Causal Structure Learningcited by 84
  2. 2021Efficient Neural Causal Discovery without Acyclicity Constraintscited by 82
  3. 2021BCD Nets: Scalable Variational Approaches for Bayesian Causal Discoverycited by 68
  4. 2018SparseMAP: Differentiable Sparse Structured Inferencecited by 62
  5. 2021DAGs with No Curl: An Efficient DAG Structure Learning Approachcited by 53
  6. 2021Unsuitability of NOTEARS for Causal Graph Discoverycited by 47
  7. 2022Differentiable DAG Samplingcited by 47
  8. 2022Large-Scale Differentiable Causal Discovery of Factor Graphscited by 47
  9. 2019Scaling structural learning with NO-BEARS to infer causal transcriptome networkscited by 39
  10. 2020On the Convergence of Continuous Constrained Optimization for Structure Learningcited by 38
  11. 2023Structure Learning with Continuous Optimization: A Sober Look and Beyondcited by 36
  12. 2019Ordering-Based Causal Structure Learning in the Presence of Latent Variablescited by 26
  13. 2022BaCaDI: Bayesian Causal Discovery with Unknown Interventionscited by 26
  14. 2020On Low Rank Directed Acyclic Graphs and Causal Structure Learningcited by 23
  15. 2022Truncated Matrix Power Iteration for Differentiable DAG Learningcited by 23
  16. 2020Efficient Marginalization of Discrete and Structured Latent Variables via Sparsitycited by 21
  17. 2023Optimizing NOTEARS Objectives via Topological Swapscited by 17
  18. 2023DAG Learning on the Permutahedroncited by 9
  19. 2022On the Sparse DAG Structure Learning Based on Adaptive Lassocited by 3

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 4; 2025: 3; 2026: 3.

10 papers.

  1. 2024Demystifying amortized causal discovery with transformerscited by 11
  2. 2024Reinforcement Learning for Causal Discovery without Acyclicity Constraintscited by 3
  3. 2025Interpretable Hierarchical Concept Reasoning through Attention-Guided Graph Learningcited by 3
  4. 2024LOCAL: Learning with Orientation Matrix to Infer Causal Structure from Time Series Datacited by 2
  5. 2024Scalable Variational Causal Discovery Unconstrained by Acyclicitycited by 1
  6. 2025Causal Discovery via Bayesian Optimizationcited by 1
  7. 2025Towards the Formalization of a Trustworthy AI for Mining Interpretable Models explOiting Sophisticated Algorithmscited by 1
  8. 2026MARLIN: Multi-Agent Reinforcement Learning for Incremental DAG Discoverycited by 0
  9. 2026Neural Autoregressive Flows for Markov Boundary Learningcited by 0
  10. 2026Support Selection Beyond Smooth DAG Exactness: Completion Geometry,Score Margins, and Selective Certificatescited by 0