Regression-based Bayesian estimation and structure learning for nonparanormal graphical models

Statistical Analysis and Data Mining

article

Jami J. Mulgrave¹  Subhashis Ghosal¹ 

[1] Department of Statistics, North Carolina State University

关键词: Bayesian inference;    Cholesky decomposition;    continuous shrinkage prior;    nonparanormal graphical models;   

DOI  :  10.1002/sam.11576

学科分类：社会科学、人文和艺术（综合）

来源: John Wiley & Sons, Inc.

【 摘 要 】

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.

【 授权许可】

Unknown