An efficient Bayesian approach for Gaussian Bayesian network structure learning

ABSTRACT This article proposes a Bayesian computing algorithm to infer Gaussian directed acyclic graphs (DAGs). It has the ability of escaping local modes and maintaining adequate computing speed compared to existing methods. Simulations demonstrated that the proposed algorithm has low false positives and false negatives in comparison to an algorithm applied to DAGs. We applied the algorithm to an epigenetic dataset to infer DAG's for smokers and nonsmokers.

[1]  Marco Grzegorczyk,et al.  Improving the structure MCMC sampler for Bayesian networks by introducing a new edge reversal move , 2008, Machine Learning.

[2]  Naftali Harris,et al.  PC algorithm for nonparanormal graphical models , 2013, J. Mach. Learn. Res..

[3]  N. Balov.  Consistent Model Selection of Discrete Bayesian Networks from Incomplete Data , 2011, 1105.4507.

[4]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[5]  David Maxwell Chickering,et al.  Large-Sample Learning of Bayesian Networks is NP-Hard , 2002, J. Mach. Learn. Res..

[6]  P. Green,et al.  Decomposable graphical Gaussian model determination , 1999 .

[7]  David Heckerman,et al.  A Tutorial on Learning with Bayesian Networks , 1999, Innovations in Bayesian Networks.

[8]  Nir Friedman,et al.  Being Bayesian About Network Structure. A Bayesian Approach to Structure Discovery in Bayesian Networks , 2004, Machine Learning.

[9]  Guido Consonni,et al.  Objective Bayesian Search of Gaussian Directed Acyclic Graphical Models for Ordered Variables with Non‐Local Priors , 2013, Biometrics.

[10]  David Maxwell Chickering,et al.  Learning Bayesian Networks: The Combination of Knowledge and Statistical Data , 1994, Machine Learning.

[11]  Faming Liang,et al.  Author's Personal Copy Computational Statistics and Data Analysis Learning Bayesian Networks for Discrete Data , 2022 .

[12]  Pedro Larrañaga,et al.  Structure Learning of Bayesian Networks by Genetic Algorithms: A Performance Analysis of Control Parameters , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[13]  Constantin F. Aliferis,et al.  The max-min hill-climbing Bayesian network structure learning algorithm , 2006, Machine Learning.

[14]  S. H. Arshad,et al.  Effect of environmental factors on the development of allergic disorders in infancy. , 1992, The Journal of allergy and clinical immunology.

[15]  Euntai Kim,et al.  A new genetic approach for structure learning of Bayesian networks: Matrix genetic algorithm , 2010 .

[16]  Andrew W. Moore,et al.  Optimal Reinsertion: A New Search Operator for Accelerated and More Accurate Bayesian Network Structure Learning , 2003, ICML.

[17]  Peter Bühlmann,et al.  Robustification of the PC-Algorithm for Directed Acyclic Graphs , 2008 .

[18]  D. Madigan,et al.  Bayesian model averaging and model selection for markov equivalence classes of acyclic digraphs , 1996 .

[19]  Remco R. Bouckaert,et al.  Properties of Bayesian Belief Network Learning Algorithms , 1994, UAI.

[20]  S. Kou,et al.  Equi-energy sampler with applications in statistical inference and statistical mechanics , 2005, math/0507080.

[21]  W. Wong,et al.  Learning Causal Bayesian Network Structures From Experimental Data , 2008 .

[22]  Tom Burr,et al.  Causation, Prediction, and Search , 2003, Technometrics.

[23]  Qing Zhou,et al.  Inferring large graphs using $$\ell _1$$ℓ1-penalized likelihood , 2011, Stat. Comput..

[24]  Thomas C. M. Lee,et al.  A Full Bayesian Approach for Boolean Genetic Network Inference , 2014, PloS one.

[25]  Qiang Ji,et al.  Efficient Structure Learning of Bayesian Networks using Constraints , 2011, J. Mach. Learn. Res..

[26]  D. Madigan,et al.  A characterization of Markov equivalence classes for acyclic digraphs , 1997 .

[27]  Qing Zhou,et al.  Learning Sparse Causal Gaussian Networks With Experimental Intervention: Regularization and Coordinate Descent , 2013 .

[28]  J. York,et al.  Bayesian Graphical Models for Discrete Data , 1995 .

[29]  David Maxwell Chickering,et al.  Learning Equivalence Classes of Bayesian Network Structures , 1996, UAI.

[30]  Susan K. Murphy,et al.  450K Epigenome-Wide Scan Identifies Differential DNA Methylation in Newborns Related to Maternal Smoking during Pregnancy , 2012, Environmental health perspectives.

[31]  S. Beach,et al.  Changes in DNA methylation at the aryl hydrocarbon receptor repressor may be a new biomarker for smoking , 2013, Clinical Epigenetics.

[32]  Peter Bühlmann,et al.  Estimating High-Dimensional Directed Acyclic Graphs with the PC-Algorithm , 2007, J. Mach. Learn. Res..

[33]  Kevin P. Murphy,et al.  Bayesian structure learning using dynamic programming and MCMC , 2007, UAI.

[34]  Ali Shojaie,et al.  Penalized likelihood methods for estimation of sparse high-dimensional directed acyclic graphs. , 2009, Biometrika.