Abstract
We first focus on recent inferential and computational techniques for multiple graphical models, where the sub-group assignment depends on the value of an external observed covariate. We then introduce Bayesian Gaussian graphical models with covariates (GGMx), a class of multivariate Gaussian distributions with covariate-dependent sparse precision matrix. We propose a general construction of a functional mapping from the covariate space to the cone of sparse positive definite matrices, that encompasses many existing graphical models for heterogeneous settings. he flexible formulation of GGMx allows both the strength and the sparsity pattern of the precision matrix (hence the graph structure) change with the covariates. Extensive simulations and a case study in cancer genomics demonstrate the utility of the proposed models. Joint work with Yang Ni, Veerabhadran Baladandayuthapani, and Claudio Busatto.