A Stepwise Approach for High-Dimensional Gaussian Graphical Models

Abstract

We present a stepwise approach to estimate high dimensional Gaussian graphicalmodels. We exploit the relation between the partial correlation coefficientsand the distribution of the prediction errors, and parametrize the model in termsof the Pearson correlation coefficients between the prediction errors of the nodes’best linear predictors. We propose a novel stepwise algorithm for detecting pairsof conditionally dependent variables. We compare the proposed algorithm withexisting methods including graphical lasso (Glasso), constrained `l1-minimization(CLIME) and equivalent partial correlation (EPC), via simulation studies andreal life applications. In our simulation study we consider several model settingsand report the results using different performance measures that look at desirablefeatures of the recovered graph.