We introduce Bayesian Gaussian graphical models with covariates (GGMx), a class ofmultivariate Gaussian distributions with covariate-dependent sparse precision matrix. Wepropose a general construction of a functional mapping from the covariate space to the coneof sparse positive definite matrices, which encompasses many existing graphical models forheterogeneous settings. Our methodology is based on a novel mixture prior for precisionmatrices with a non-local component that admits attractive theoretical and empirical prop-erties. The flexible formulation of GGMx allows both the strength and the sparsity patternof the precision matrix (hence the graph structure) change with the covariates. Posteriorinference is carried out with a carefully designed Markov chain Monte Carlo algorithm,which ensures the positive definiteness of sparse precision matrices at any given covariates’values. Extensive simulations and a case study in cancer genomics demonstrate the utilityof the proposed model

Bayesian Covariate-Dependent Gaussian Graphical Models with Varying Structure / Yang Ni, Francesco Stingo, Veerabhadran Baladandayuthapani. - In: JOURNAL OF MACHINE LEARNING RESEARCH. - ISSN 1532-4435. - ELETTRONICO. - 23:(2022), pp. 1-29.

Bayesian Covariate-Dependent Gaussian Graphical Models with Varying Structure

Francesco Stingo;
2022

Abstract

We introduce Bayesian Gaussian graphical models with covariates (GGMx), a class ofmultivariate Gaussian distributions with covariate-dependent sparse precision matrix. Wepropose a general construction of a functional mapping from the covariate space to the coneof sparse positive definite matrices, which encompasses many existing graphical models forheterogeneous settings. Our methodology is based on a novel mixture prior for precisionmatrices with a non-local component that admits attractive theoretical and empirical prop-erties. The flexible formulation of GGMx allows both the strength and the sparsity patternof the precision matrix (hence the graph structure) change with the covariates. Posteriorinference is carried out with a carefully designed Markov chain Monte Carlo algorithm,which ensures the positive definiteness of sparse precision matrices at any given covariates’values. Extensive simulations and a case study in cancer genomics demonstrate the utilityof the proposed model
2022
23
1
29
Yang Ni, Francesco Stingo, Veerabhadran Baladandayuthapani
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1282708
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