Assessment of Covariance Selection Methods in High-Dimensional Gaussian Graphical Models

Abstract

The covariance selection in Gaussian graphical models consists in selecting, based on a sample of a multivariate normal vector, all those pairs of variables that are conditionally dependent given the remaining variables. This problem is equivalent to estimate the graph identifying the nonzero elements on the off-diagonal entries of the precision matrix. There are different proposals to carry out covariance selection in high-dimensional Gaussian graphical models, such as neighborhood selection and Glasso, among others. In this paper we introduce a methodology for evaluating the performance of graph estimators, defining the notion of non-informative estimator. Through a simulation study, the empirical behavior of Glasso in different structures of the precision matrix is investigated and its performance is analyzed according to different degrees of density of the graph. Our proposal can be used for other covariance selection methods.