Graph_sampler: a simple tool for fully Bayesian analyses of DAG-models

Bayesian networks (BNs) are widely used graphical models usable to draw statistical inference about directed acyclic graphs. We presented here Graph_sampler a fast free C language software for structural inference on BNs. Graph_sampler uses a fully Bayesian approach in which the marginal likelihood of the data and prior information about the network structure are considered. This new software can handle both the continuous as well as discrete data and based on the data type two different models are formulated. The software also provides a wide variety of structure prior which can depict either the global or local properties of the graph structure. Now based on the type of structure prior selected, we considered a wide range of possible values for the prior making it either informative or uninformative. We proposed a new and much faster jumping kernel strategy in the Metropolis–Hastings algorithm. The source C code distributed is very compact, fast, uses low memory and disk storage. We performed out several analyses based on different simulated data sets and synthetic as well as real networks to discuss the performance of Graph_sampler.

[1]  Sach Mukherjee,et al.  Network inference using informative priors , 2008, Proceedings of the National Academy of Sciences.

[2]  Marco Scutari,et al.  Learning Bayesian Networks with the bnlearn R Package , 2009, 0908.3817.

[3]  Christian P. Robert,et al.  Monte Carlo Statistical Methods (Springer Texts in Statistics) , 2005 .

[4]  Ghislaine Gayraud,et al.  Probabilistic Generation of Random Networks Taking into Account Information on Motifs Occurrence , 2013, J. Comput. Biol..

[5]  Dirk Husmeier,et al.  Sensitivity and specificity of inferring genetic regulatory interactions from microarray experiments with dynamic Bayesian networks , 2003, Bioinform..

[6]  D. Edwards Introduction to graphical modelling , 1995 .

[7]  Steffen L. Lauritzen,et al.  Graphical models in R , 1996 .

[8]  Sach Mukherjee,et al.  MC4: A Tempering Algorithm for Large-Sample Network Inference , 2010, PRIB.

[9]  Kevin B. Korb,et al.  Bayesian Artificial Intelligence , 2004, Computer science and data analysis series.

[10]  Paul H. J. Kelly,et al.  A dynamic topological sort algorithm for directed acyclic graphs , 2007, ACM J. Exp. Algorithmics.

[11]  Kevin B. Korb,et al.  Bayesian Artificial Intelligence, Second Edition , 2010 .

[12]  Christian P. Robert,et al.  Monte Carlo Statistical Methods , 2005, Springer Texts in Statistics.

[13]  Kevin Murphy Software for Graphical models : a review by , 2007 .

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

[15]  Claus Dethlefsen,et al.  deal: A Package for Learning Bayesian Networks , 2003 .

[16]  Richard E. Neapolitan,et al.  Probabilistic reasoning in expert systems - theory and algorithms , 2012 .

[17]  Matthew J. Beal,et al.  The variational Bayesian EM algorithm for incomplete data: with application to scoring graphical model structures , 2003 .

[18]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[19]  Richard E. Neapolitan,et al.  Learning Bayesian networks , 2007, KDD '07.

[20]  Steen Andreassen,et al.  Using probabilistic and decision-theoretic methods in treatment and prognosis modeling , 1999, Artif. Intell. Medicine.

[21]  Kevin P. Murphy,et al.  Learning the Structure of Dynamic Probabilistic Networks , 1998, UAI.

[22]  P. Green,et al.  Bayesian Variable Selection and the Swendsen-Wang Algorithm , 2004 .

[23]  D. Rubin,et al.  Inference from Iterative Simulation Using Multiple Sequences , 1992 .