Graphiclasso: Graphical lasso for learning sparse inverse-covariance matrices

Abstract

In modern multivariate statistics, where high-dimensional datasets are ubiquitous, learning large (inverse-) covariance matrices is imperative for data analysis. A popular approach to estimating a large inverse-covariance matrix is to regularize the Gaussian log-likelihood function by imposing a convex penalty function. In a seminal article, Friedman, Hastie, and Tibshirani (2008, Biostatistics 9: 432–441) proposed a graphical lasso (Glasso) algorithm to efficiently estimate sparse inverse-covariance matrices from the convex regularized log-likelihood function. In this article, I first explore the Glasso algorithm and then introduce a new graphiclasso command for the large inverse-covariance matrix estimation. Moreover, I provide a useful command for tuning parameter selection in the Glasso algorithm using the extended Bayesian information criterion, the Akaike information criterion, and cross-validation. I demonstrate the use of Glasso using simulation results and real-world data analysis.