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Covariance graphical lasso applies a lasso penalty on the elements of thecovariance matrix. This method is useful because it not only produces sparseestimation of covariance matrix but also discovers marginal independencestructures by generating zeros in the covariance matrix. We propose and exploretwo new algorithms for solving the covariance graphical lasso problem. Our newalgorithms are based on coordinate descent and ECM. We show that these twoalgorithms are more attractive than the only existing competing algorithm ofBien and Tibshirani (2011) in terms of simplicity, speed and stability. We alsodiscuss convergence properties of our algorithms.

Two New Algorithms for Solving Covariance Graphical Lasso Based on Coordinate Descent and ECM