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We consider estimation of undirected Gaussian graphical models and inversecovariances in high-dimensional scenarios by penalizing the correspondingprecision matrix. While single $L_1$ (Graphical Lasso) and $L_2$ (GraphicalRidge) penalties for the precision matrix have already been studied, we proposethe combination of both, yielding an Elastic Net type penalty. We enableadditional flexibility by allowing to include diagonal target matrices for theprecision matrix. We generalize existing algorithms for the Graphical Lasso andprovide corresponding software with an efficient implementation to facilitateusage for practitioners. Our software borrows computationally favorable partsfrom a number of existing packages for the Graphical Lasso, leading to anoverall fast(er) implementation and at the same time yielding also much moremethodological flexibility.

Graphical Elastic Net and Target Matrices: Fast Algorithms and Software for Sparse Precision Matrix Estimation