mlsanityData to 7 Oct 2026

CoLiDE: Concomitant Linear DAG Estimation

arXiv 2310.02895 ↗First posted 4 Oct 2023cs.LGcited by 12

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Abstract (arXiv)

We deal with the combinatorial problem of learning directed acyclic graph (DAG) structure from observational data adhering to a linear structural equation model (SEM). Leveraging advances in differentiable, nonconvex characterizations of acyclicity, recent efforts have advocated a continuous constrained optimization paradigm to efficiently explore the space of DAGs. Most existing methods employ lasso-type score functions to guide this search, which (i) require expensive penalty parameter retuning when the textitunknown SEM noise variances change across problem instances; and (ii) implicitly rely on limiting homoscedasticity assumptions. In this work, we propose a new convex score function for sparsity-aware learning of linear DAGs, which incorporates concomitant estimation of scale and thus effectively decouples the sparsity parameter from the exogenous noise levels. Regularization via a smooth, nonconvex acyclicity penalty term yields CoLiDE (Concomitant Linear DAG Estimation), a regression-based criterion amenable to efficient gradient computation and closed-form estimation of noise variances in heteroscedastic scenarios. Our algorithm outperforms state-of-the-art methods without incurring added complexity, especially when the DAGs are larger and the noise level profile is heterogeneous. We also find CoLiDE exhibits enhanced stability manifested via reduced standard deviations in several domain-specific metrics, underscoring the robustness of our novel linear DAG estimator.

Key facts. Cited by 12 papers in the map (data through 7 Oct 2026). Builds on 27 of its 59 references that are in the map. First posted on arXiv 4 Oct 2023.

Builds on

27 of 59 references.

References · 27

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15 more
  1. 2019Permutation-Based Causal Structure Learning with Unknown Intervention Targetscited by 69
  2. 2021BCD Nets: Scalable Variational Approaches for Bayesian Causal Discoverycited by 68
  3. 2020DAGs with No Fears: A Closer Look at Continuous Optimization for Learning Bayesian Networkscited by 66
  4. 2022Differentiable DAG Samplingcited by 46
  5. 2020Towards Scalable Bayesian Learning of Causal DAGscited by 33
  6. 2020Efficient Intervention Design for Causal Discovery with Latentscited by 22
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  11. 2023Global Optimality in Bivariate Gradient-based DAG Learningcited by 10
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Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 3; 2025: 4; 2026: 5.

12 papers.

  1. 2024Non-negative Weighted DAG Structure Learningcited by 7
  2. 2024Convolutional Learning on Directed Acyclic Graphscited by 6
  3. 2025BUILD with Precision: Bottom-Up Inference of Linear DAGscited by 4
  4. 2026Exploiting Non-Negativity in DAG Structure Learningcited by 3
  5. 2026Concomitant DAG Learning: On the Roles of Noise Adaptivity, Sparsity, and Non-negativitycited by 2
  6. 2024Revisiting Differentiable Structure Learning: Inconsistency of ℓ1 Penalty and Beyondcited by 1
  7. 2025Directed Acyclic Graph Convolutional Networkscited by 1
  8. 2025Non-negative DAG Learning from Time-Series Datacited by 0
  9. 2025Topology Identification and Inference over Graphscited by 0
  10. 2026Directed Graph Topology Inference via Graph Filter Identificationcited by 0
  11. 2026From topology learning to graph generation: A unifying perspectivecited by 0
  12. 2026Nonnegative DAG Learning via Concomitant Estimationcited by 0