mlsanityData to 7 Oct 2026

High-dimensional consistency in score-based and hybrid structure learning

arXiv 1507.02608 ↗First posted 9 Jul 2015math.ST stat.ME stat.THcited by 44

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Abstract (arXiv)

Main approaches for learning Bayesian networks can be classified as constraint-based, score-based or hybrid methods. Although high-dimensional consistency results are available for constraint-based methods like the PC algorithm, such results have not been proved for score-based or hybrid methods, and most of the hybrid methods have not even shown to be consistent in the classical setting where the number of variables remains fixed and the sample size tends to infinity. In this paper, we show that consistency of hybrid methods based on greedy equivalence search (GES) can be achieved in the classical setting with adaptive restrictions on the search space that depend on the current state of the algorithm. Moreover, we prove consistency of GES and adaptively restricted GES (ARGES) in several sparse high-dimensional settings. ARGES scales well to sparse graphs with thousands of variables and our simulation study indicates that both GES and ARGES generally outperform the PC algorithm.

Key facts. Cited by 44 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Jul 2015.

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Citing papers per year: 2021: 11; 2022: 9; 2023: 7; 2024: 8; 2025: 5; 2026: 4.

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  2. 2021A survey of Bayesian Network structure learningcited by 85
  3. 2023A Survey on Causal Discovery: Theory and Practicecited by 63
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  10. 2023DRCFS: Doubly Robust Causal Feature Selectioncited by 12
  11. 2024Gene Regulatory Network Inference in the Presence of Dropouts: a Causal Viewcited by 11
  12. 2021Structure learning in polynomial time: Greedy algorithms, Bregman information, and exponential familiescited by 10
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  6. 2021A Fast Non-parametric Approach for Local Causal Structure Learningcited by 5
  7. 2023iSCAN: Identifying Causal Mechanism Shifts among Nonlinear Additive Noise Modelscited by 5
  8. 2021Partitioned hybrid learning of Bayesian network structurescited by 4
  9. 2024Causal Discovery over High-Dimensional Structured Hypothesis Spaces with Causal Graph Partitioningcited by 4
  10. 2025Embracing Discrete Search: A Reasonable Approach to Causal Structure Learningcited by 4
  11. 2024Optimal estimation of Gaussian (poly)treescited by 3
  12. 2024CIDGMed: Causal Inference-Driven Medication Recommendation with Enhanced Dual-Granularity Learningcited by 3
  13. 2022VAC2: Visual Analysis of Combined Causality in Event Sequencescited by 2
  14. 2022Reframed GES with a Neural Conditional Dependence Measurecited by 2
  15. 2024Greedy equivalence search for nonparametric graphical modelscited by 2
  16. 2025Causal Discovery on Higher-Order Interactionscited by 2
  17. 2026Score-Based Causal Discovery of Latent Variable Causal Modelscited by 2
  18. 2021Improving Accuracy of Permutation DAG Search using Best Order Score Searchcited by 1
  19. 2021Efficient Learning of Quadratic Variance Function Directed Acyclic Graphs via Topological Layerscited by 1
  20. 2022From Causal Pairs to Causal Graphscited by 1
  21. 2023Data-Driven Estimation of Heterogeneous Treatment Effectscited by 1
  22. 2024An Asymptotically Optimal Coordinate Descent Algorithm for Learning Bayesian Networks from Gaussian Modelscited by 1
  23. 2025Score-based Greedy Search for Structure Identification of Partially Observed Linear Causal Modelscited by 1
  24. 2026On the Number of Conditional Independence Tests in Constraint-based Causal Discoverycited by 1
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  26. 2021Identifiability of AMP chain graph modelscited by 0
  27. 2022Estimating large causal polytrees from small samplescited by 0
  28. 2023Distributionally Robust Skeleton Learning of Discrete Bayesian Networkscited by 0
  29. 2024Membership Testing in Markov Equivalence Classes via Independence Query Oraclescited by 0
  30. 2025Optimal structure learning and conditional independence testingcited by 0
  31. 2026A Survey on Federated Causal Discovery and Inferencecited by 0
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