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On Causal Discovery with Equal Variance Assumption

arXiv 1807.03419 ↗First posted 9 Jul 2018stat.ME stat.COcited by 59

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Abstract (arXiv)

Prior work has shown that causal structure can be uniquely identified from observational data when these follow a structural equation model whose error terms have equal variances. We show that this fact is implied by an ordering among (conditional) variances. We demonstrate that ordering estimates of these variances yields a simple yet state-of-the-art method for causal structure learning that is readily extendable to high-dimensional problems.

Key facts. Cited by 59 papers in the map (data through 14 Oct 2026). First posted on arXiv 9 Jul 2018.

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Citing papers per year: 2021: 10; 2022: 6; 2023: 16; 2024: 7; 2025: 9; 2026: 11.

59 papers.

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  1. 2021Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Gamecited by 161
  2. 2022Diffusion Models for Causal Discovery via Topological Orderingcited by 66
  3. 2021DAGs with No Curl: An Efficient DAG Structure Learning Approachcited by 53
  4. 2023A Scale-Invariant Sorting Criterion to Find a Causal Order in Additive Noise Modelscited by 28
  5. 2023textttcausalAssembly: Generating Realistic Production Data for Benchmarking Causal Discoverycited by 18
  6. 2022Optimal estimation of Gaussian DAG modelscited by 17
  7. 2023Optimizing NOTEARS Objectives via Topological Swapscited by 17
  8. 2024Adjustment Identification Distance: A gadjid for Causal Structure Learningcited by 16
  9. 2021Efficient Bayesian network structure learning via local Markov boundary searchcited by 14
  10. 2021Structure learning in polynomial time: Greedy algorithms, Bregman information, and exponential familiescited by 11
  11. 2022Valid Inference After Causal Discoverycited by 10
  12. 2023Global Optimality in Bivariate Gradient-based DAG Learningcited by 10
38 more
  1. 2023Effective Causal Discovery under Identifiable Heteroscedastic Noise Modelcited by 10
  2. 2025Unitless Unrestricted Markov-Consistent SCM Generation: Better Benchmark Datasets for Causal Discoverycited by 8
  3. 2023Heteroscedastic Causal Structure Learningcited by 7
  4. 2021Learning linear non-Gaussian directed acyclic graph with diverging number of nodescited by 6
  5. 2023Structural restrictions in local causal discovery: identifying direct causes of a target variablecited by 5
  6. 2023Order-based Structure Learning with Normalizing Flowscited by 5
  7. 2026Causal Representation Learning from General Environments under Nonparametric Mixingcited by 5
  8. 2024Integer Programming for Learning Directed Acyclic Graphs from Non-identifiable Gaussian Modelscited by 4
  9. 2025BUILD with Precision: Bottom-Up Inference of Linear DAGscited by 4
  10. 2022Sequentially learning the topological ordering of causal directed acyclic graphs with likelihood ratio scorescited by 3
  11. 2023dotears: Scalable, consistent DAG estimation using observational and interventional datacited by 3
  12. 2023Differentiable Bayesian Structure Learning with Acyclicity Assurancecited by 3
  13. 2024Optimal estimation of Gaussian (poly)treescited by 3
  14. 2024Reinforcement Learning for Causal Discovery without Acyclicity Constraintscited by 3
  15. 2025Learning Gaussian DAG Models without Condition Number Boundscited by 3
  16. 2021Learning Sparse Fixed-Structure Gaussian Bayesian Networkscited by 2
  17. 2022Correcting Confounding via Random Selection of Background Variablescited by 2
  18. 2023Information Theoretically Optimal Sample Complexity of Learning Dynamical Directed Acyclic Graphscited by 2
  19. 2024Learning Directed Acyclic Graphs from Partial Orderingscited by 2
  20. 2025Causal Ordering for Structure Learning from Time Seriescited by 2
  21. 2026Contrast-Free ICA and Causal Inference via Wasserstein Distances to the Gaussiancited by 2
  22. 2026Causal Discovery in Equal Variance Linear Gaussian DAGs via SURE-Tuned Ridge Regressioncited by 2
  23. 2021Causal Identification with Additive Noise Models: Quantifying the Effect of Noisecited by 1
  24. 2021Efficient Learning of Quadratic Variance Function Directed Acyclic Graphs via Topological Layerscited by 1
  25. 2022Learning Large Causal Structures from Inverse Covariance Matrix via Sparse Matrix Decompositioncited by 1
  26. 2023Recovering Linear Causal Models with Latent Variables via Cholesky Factorization of Covariance Matrixcited by 1
  27. 2024Generalized Criterion for Identifiability of Additive Noise Models Using Majorizationcited by 1
  28. 2024An Asymptotically Optimal Coordinate Descent Algorithm for Learning Bayesian Networks from Gaussian Modelscited by 1
  29. 2025Identifiability of the minimum-trace directed acyclic graph and hill climbing algorithms without strict local optima under weakly increasing error variancescited by 1
  30. 2025Consistent Bayesian causal discovery for structural equation models with equal error variancescited by 1
  31. 2026Ordering-based Causal Discovery via Generalized Score Matchingcited by 1
  32. 2021Identifiability of AMP chain graph modelscited by 0
  33. 2021The Effect of Noise Level on Causal Identification with Additive Noise Modelscited by 0
  34. 2023Structural transfer learning of non-Gaussian DAGcited by 0
  35. 2023Distributionally Robust Skeleton Learning of Discrete Bayesian Networkscited by 0
  36. 2023Bayesian Approach to Linear Bayesian Networkscited by 0
  37. 2023Inconsistency of cross-validation for structure learning in Gaussian graphical modelscited by 0
  38. 2025Sparsity-Induced Global Matrix Autoregressive Model with Auxiliary Network Datacited by 0

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