mlsanityData to 14 Oct 2026

A Topological Sorting Criterion for Random Causal Directed Acyclic Graphs

arXiv 2605.06288 ↗First posted 7 May 2026stat.ME cs.AIcited by 0

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Abstract (arXiv)

Random directed acyclic graphs (DAGs) based on imposing an order on ErdHos-R'enyi and scale free random graphs are widely used for evaluating causal discovery algorithms. We show that in such DAGs, the set of nodes reachable via open paths, termed relatives, increases monotonically along the causal order. We assess the prevalence of this pattern numerically, and demonstrate that it can be exploited for causal order recovery via sorting by the estimated number of relatives. We note that many simulations in the literature feature settings where this yields an excellent proxy for the causal order, and show that a strict increase of relatives along the causal order leads to a singular Markov equivalence class. We propose sampling time-series DAGs as a possible alternative and discuss implications for causal discovery algorithms and their evaluation on synthetic data.

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References · 37

  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. 2013Causal Discovery with Continuous Additive Noise Modelscited by 255
  4. 2019Gradient-Based Neural DAG Learningcited by 227
  5. 2020Differentiable Causal Discovery from Interventional Datacited by 218
  6. 2021D'ya like DAGs? A Survey on Structure Learning and Causal Discoverycited by 211
  7. 2020On the Role of Sparsity and DAG Constraints for Learning Linear DAGscited by 191
  8. 2013CAM: Causal additive models, high-dimensional order search and penalized regressioncited by 178
  9. 2013Causal Inference and Causal Explanation with Background Knowledgecited by 170
  10. 2021Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Gamecited by 161
  11. 2022Bayesian Structure Learning with Generative Flow Networkscited by 153
  12. 2022DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterizationcited by 140
25 more
  1. 2022Score matching enables causal discovery of nonlinear additive noise modelscited by 111
  2. 2021DiBS: Differentiable Bayesian Structure Learningcited by 106
  3. 2021A survey of Bayesian Network structure learningcited by 87
  4. 2017Causal Structure Learningcited by 84
  5. 2023Scalable Causal Discovery with Score Matchingcited by 45
  6. 2023Structure Learning with Continuous Optimization: A Sober Look and Beyondcited by 36
  7. 2023CausalTime: Realistically Generated Time-series for Benchmarking of Causal Discoverycited by 36
  8. 2020Towards Scalable Bayesian Learning of Causal DAGscited by 33
  9. 2023BayesDAG: Gradient-Based Posterior Inference for Causal Discoverycited by 33
  10. 2019The Case for Evaluating Causal Models Using Interventional Measures and Empirical Datacited by 30
  11. 2023A Scale-Invariant Sorting Criterion to Find a Causal Order in Additive Noise Modelscited by 28
  12. 2016Ancestral Causal Inferencecited by 24
  13. 2024A Meta-Learning Approach to Bayesian Causal Discoverycited by 22
  14. 2023textttcausalAssembly: Generating Realistic Production Data for Benchmarking Causal Discoverycited by 18
  15. 2024The Landscape of Causal Discovery Data: Grounding Causal Discovery in Real-World Applicationscited by 18
  16. 2024Standardizing Structural Causal Modelscited by 17
  17. 2024Adjustment Identification Distance: A gadjid for Causal Structure Learningcited by 16
  18. 2023Do we become wiser with time? On causal equivalence with tiered background knowledgecited by 9
  19. 2025Unitless Unrestricted Markov-Consistent SCM Generation: Better Benchmark Datasets for Causal Discoverycited by 8
  20. 2024Better Simulations for Validating Causal Discovery with the DAG-Adaptation of the Onion Methodcited by 6
  21. 2024Large-Scale Targeted Cause Discovery via Learning from Simulated Datacited by 6
  22. 2025Embracing Discrete Search: A Reasonable Approach to Causal Structure Learningcited by 4
  23. 2025The Case for Time in Causal DAGscited by 3
  24. 2025Benchmarking Constraint-Based Bayesian Structure Learning Algorithms: Role of Network Topologycited by 1
  25. 2025Lower Bounds on the Size of Markov Equivalence Classescited by 1

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