Abstract: Graphical models is an important tool to study the relationship among variables. Besides the node variables, the additional covariates are frequently recorded together with the data and may influence the dependence relationships. However, most of the existing work on graphical models only considers the node variables. In this paper, we study the problem of reconstructing network structure from the data with covariates by applying the tools of graphical models. In the framework of sparse regularization, we propose a novel sparse Gaussian graphical models to incorporate the covariates information, where the conditional independency relationship between variables are assumed to be a linear function of the covariates. The proposed model is interpretable and easy to solve. We employ the coordinate descent algorithm to solve the model. A series of numerical examples shows that the effect of the covariate is better than that of the non covariate, which indicates the effectiveness and efficiency of the proposed model.

Key words: graphical models, sparse, regularization, covariates, SCAD