Regression‐based Bayesian estimation and structure learning for nonparanormal graphical models. (28th February 2022)

• Record Type: Journal Article
• Authors: Mulgrave, Jami J.; Ghosal, Subhashis
• Is Part Of: Statistical analysis and data mining. Volume 15:Number 5(2022)
• Page Start: 611
• Page End: 629
• Publication Date: 2022-02-28
• Subjects: Bayesian inference -- Cholesky decomposition -- continuous shrinkage prior -- nonparanormal graphical models; Data mining -- Statistical methods -- Periodicals; 006.312
• DOI: 10.1002/sam.11576
• Languages: English
• ISSNs: 1932-1864

Abstract

Abstract: 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 to inference in a nonparanormal graphical model in which we put priors on the unknown transformations through a 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 coefficients. 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 microarray dataset. The proposed methods have better performance as the dimension increases, and in particular, the variational Bayesian approach has the potential to speed up the estimation in the Bayesian nonparanormal graphical model without the Gaussianity assumption while retaining the information to construct the graph.