Regression Based Bayesian Approach for Nonparanormal Graphical Models
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A nonparanormal graphical model is a semiparametric generalization of a Gaussian graphical model for continuous variables in which it is assumed that the variables follow a Gaussian graphical model only after some unknown smooth monotone transformations. We consider a Bayesian approach in the nonparanormal graphical model in which we put priors on the unknown transformations through random series based on B-splines. We use a regression formulation to construct the likelihood through the Cholesky decomposition on the underlying precision matrix of the transformed variables and put shrinkage priors on the regression coefcients. We apply a plug-in variational Bayesian algorithm for learning the sparse precision matrix and compare the performance to a posterior Gibbs sampling scheme in a simulation study. We finally apply the proposed methods to a real data set.
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