Regression-Based Bayesian Estimation and Structure Learning for Nonparanormal Graphical Models
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 real data set. KEYWORDS:
Cite
@article{arxiv.1812.04442,
title = {Regression-Based Bayesian Estimation and Structure Learning for Nonparanormal Graphical Models},
author = {Jami J. Mulgrave and Subhashis Ghosal},
journal= {arXiv preprint arXiv:1812.04442},
year = {2021}
}
Comments
arXiv admin note: text overlap with arXiv:1812.02884