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We present a stepwise approach to estimate high dimensional Gaussiangraphical models. We exploit the relation between the partial correlationcoefficients and the distribution of the prediction errors, and parametrize themodel in terms of the Pearson correlation coefficients between the predictionerrors of the nodes' best linear predictors. We propose a novel stepwisealgorithm for detecting pairs of conditionally dependent variables. We showthat the proposed algorithm outperforms existing methods such as the graphicallasso and CLIME in simulation studies and real life applications. In ourcomparison we report different performance measures that look at differentdesirable features of the recovered graph and consider several model settings.

A Stepwise Approach for High-Dimensional Gaussian Graphical Models