mlsanityData to 7 Oct 2026

High-dimensional learning of linear causal networks via inverse covariance estimation

arXiv 1311.3492 ↗First posted 14 Nov 2013stat.ML math.ST stat.THcited by 86

Not on the map. Why?

Abstract (arXiv)

We establish a new framework for statistical estimation of directed acyclic graphs (DAGs) when data are generated from a linear, possibly non-Gaussian structural equation model. Our framework consists of two parts: (1) inferring the moralized graph from the support of the inverse covariance matrix; and (2) selecting the best-scoring graph amongst DAGs that are consistent with the moralized graph. We show that when the error variances are known or estimated to close enough precision, the true DAG is the unique minimizer of the score computed using the reweighted squared l_2-loss. Our population-level results have implications for the identifiability of linear SEMs when the error covariances are specified up to a constant multiple. On the statistical side, we establish rigorous conditions for high-dimensional consistency of our two-part algorithm, defined in terms of a "gap" between the true DAG and the next best candidate. Finally, we demonstrate that dynamic programming may be used to select the optimal DAG in linear time when the treewidth of the moralized graph is bounded.

Key facts. Cited by 86 papers in the map (data through 7 Oct 2026). First posted on arXiv 14 Nov 2013.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 11; 2022: 13; 2023: 26; 2024: 15; 2025: 11; 2026: 10.

86 papers.

Sort:

By area:

  1. 2021Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Gamecited by 159
  2. 2022DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterizationcited by 135
  3. 2022Score matching enables causal discovery of nonlinear additive noise modelscited by 108
  4. 2022Deep End-to-end Causal Inferencecited by 93
  5. 2024Causal Representation Learning from Multiple Distributions: A General Settingcited by 67
  6. 2021Unsuitability of NOTEARS for Causal Graph Discoverycited by 46
  7. 2023Structure Learning with Continuous Optimization: A Sober Look and Beyondcited by 34
  8. 2023Stable Differentiable Causal Discoverycited by 30
  9. 2023A Scale-Invariant Sorting Criterion to Find a Causal Order in Additive Noise Modelscited by 28
  10. 2022Truncated Matrix Power Iteration for Differentiable DAG Learningcited by 23
  11. 2022Reliable Causal Discovery with Improved Exact Search and Weaker Assumptionscited by 19
  12. 2024Sample, estimate, aggregate: A recipe for causal discovery foundation modelscited by 19
38 more
  1. 2023Optimizing NOTEARS Objectives via Topological Swapscited by 17
  2. 2024Standardizing Structural Causal Modelscited by 17
  3. 2021Simultaneous Missing Value Imputation and Structure Learning with Groupscited by 16
  4. 2022Optimal estimation of Gaussian DAG modelscited by 14
  5. 2021Entropic Causal Inference: Identifiability and Finite Sample Resultscited by 12
  6. 2022Causal Fourier Analysis on Directed Acyclic Graphs and Posetscited by 12
  7. 2023CoLiDE: Concomitant Linear DAG Estimationcited by 12
  8. 2023Bivariate Causal Discovery using Bayesian Model Selectioncited by 11
  9. 2024Ordering-Based Causal Discovery for Linear and Nonlinear Relationscited by 11
  10. 2021Structure learning in polynomial time: Greedy algorithms, Bregman information, and exponential familiescited by 10
  11. 2023Global Optimality in Bivariate Gradient-based DAG Learningcited by 10
  12. 2023Constraint-Free Structure Learning with Smooth Acyclic Orientationscited by 10
  13. 2021Deconfounded Score Method: Scoring DAGs with Dense Unobserved Confoundingcited by 9
  14. 2023Learning DAGs from Data with Few Root Causescited by 8
  15. 2024DCILP: A Distributed Approach for Large-Scale Causal Structure Learningcited by 8
  16. 2022Multiscale Causal Structure Learningcited by 7
  17. 2023Generalized Precision Matrix for Scalable Estimation of Nonparametric Markov Networkscited by 7
  18. 2024Local Causal Discovery with Linear non-Gaussian Cyclic Modelscited by 7
  19. 2024Non-negative Weighted DAG Structure Learningcited by 7
  20. 2024Markov Equivalence and Consistency in Differentiable Structure Learningcited by 6
  21. 2021On the Role of Entropy-based Loss for Learning Causal Structures with Continuous Optimizationcited by 5
  22. 2021A Fast Non-parametric Approach for Local Causal Structure Learningcited by 5
  23. 2022Directed Acyclic Graph Structure Learning from Dynamic Graphscited by 5
  24. 2023Boosting Differentiable Causal Discovery via Adaptive Sample Reweightingcited by 5
  25. 2023iSCAN: Identifying Causal Mechanism Shifts among Nonlinear Additive Noise Modelscited by 5
  26. 2025Analytic DAG Constraints for Differentiable DAG Learningcited by 5
  27. 2023Discovering Dynamic Causal Space for DAG Structure Learningcited by 4
  28. 2025CausalMan: A physics-based simulator for large-scale causalitycited by 4
  29. 2025The Robustness of Differentiable Causal Discovery in Misspecified Scenarioscited by 4
  30. 2025BUILD with Precision: Bottom-Up Inference of Linear DAGscited by 4
  31. 2022Learning Multiscale Non-stationary Causal Structurescited by 3
  32. 2023dotears: Scalable, consistent DAG estimation using observational and interventional datacited by 3
  33. 2023Deception by Omission: Using Adversarial Missingness to Poison Causal Structure Learningcited by 3
  34. 2024Optimal estimation of Gaussian (poly)treescited by 3
  35. 2024psiDAG: Projected Stochastic Approximation Iteration for DAG Structure Learningcited by 3
  36. 2025Entropic Causal Inference: Graph Identifiabilitycited by 3
  37. 2026Exploiting Non-Negativity in DAG Structure Learningcited by 3
  38. 2023Multi-Fidelity Covariance Estimation in the Log-Euclidean Geometrycited by 2

50 most cited of 86 All 86 (JSON)