mlsanityData to 14 Oct 2026

Bayesian Approach to Linear Bayesian Networks

arXiv 2311.15610 ↗First posted 27 Nov 2023stat.ML cs.LG math.STcited by 0

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Abstract (arXiv)

This study proposes the first Bayesian approach for learning high-dimensional linear Bayesian networks. The proposed approach iteratively estimates each element of the topological ordering from backward and its parent using the inverse of a partial covariance matrix. The proposed method successfully recovers the underlying structure when Bayesian regularization for the inverse covariance matrix with unequal shrinkage is applied. Specifically, it shows that the number of samples n = Omega( dM2 log p) and n = Omega(dM2 p2/m) are sufficient for the proposed algorithm to learn linear Bayesian networks with sub-Gaussian and 4m-th bounded-moment error distributions, respectively, where p is the number of nodes and dM is the maximum degree of the moralized graph. The theoretical findings are supported by extensive simulation studies including real data analysis. Furthermore the proposed method is demonstrated to outperform state-of-the-art frequentist approaches, such as the BHLSM, LISTEN, and TD algorithms in synthetic data.

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References · 11

  1. 2013High-dimensional learning of linear causal networks via inverse covariance estimationcited by 87
  2. 2018On Causal Discovery with Equal Variance Assumptioncited by 59
  3. 2017Learning linear structural equation models in polynomial time and sample complexitycited by 51
  4. 2020Towards Scalable Bayesian Learning of Causal DAGscited by 33
  5. 2017Learning Identifiable Gaussian Bayesian Networks in Polynomial Time and Sample Complexitycited by 27
  6. 2017Learning Quadratic Variance Function (QVF) DAG models via OverDispersion Scoring (ODS)cited by 18
  7. 2022Optimal estimation of Gaussian DAG modelscited by 17
  8. 2013A Bayesian Approach to Learning Bayesian Networks with Local Structurecited by 15
  9. 2018Bayesian Regularization for Graphical Models with Unequal Shrinkagecited by 5
  10. 2015Scaling It Up: Stochastic Search Structure Learning in Graphical Modelscited by 4
  11. 2021Efficient Learning of Quadratic Variance Function Directed Acyclic Graphs via Topological Layerscited by 1

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