A1270
Title: Covariate-adjusted Gaussian graphical models via natural parametrization
Authors: Ruobin Liu - University of California, Santa Barbara (United States) [presenting]
Guo Yu - University of California Santa Barbara (United States)
Abstract: Gaussian graphical models are widely used to recover the conditional independence structure among random variables. Recently, several key advances have been made to exploit an additional set of variables to estimate the graphical model of the variables of interest better. For example, in co-expression quantitative trait locus studies, both the mean expression level of genes and their pairwise conditional independence structure may be adjusted by genetic variants local to those genes. Existing methods to estimate covariate-adjusted graphical models either allow only the mean to depend on covariates or suffer from poor scaling assumptions due to the inherent non-convexity of simultaneously estimating the mean and precision matrix. A convex formulation that jointly estimates the covariate-adjusted mean and precision matrix is proposed by utilizing the natural parametrization of the multivariate Gaussian likelihood. This convexity yields theoretically better performance as the sparsity and dimension of the covariates grow large relative to the number of samples. The theoretical results are verified with numerical simulations and a reanalysis of a study of glioblastoma multiforme is performed.
