Graphical Models for Sparse Data: Graphical Gaussian Models with Vertex and Edge Symmetries

Abstract

The models we consider, generically denoted RCOX models, are a special class of graphical Gaussian models. In RCOX models specific elements of the concentration/partial correlation matrix can be restricted to being identical which reduces the number of parameters to be estimated. Thereby these models can be applied to problems where the number of variables is substantially larger than the number of samples. This paper outlines the fundamental concepts and ideas behind the models but focuses on model selection. Inference in RCOX models is facilitated by the R package gRc.