First-order methods for sparse covariance selection

Given a sample covariance matrix, we solve a maximum likelihood problem penalized by the number of nonzero coefficients in the inverse covariance matrix. Our objective is to find a sparse representation of the sample data and to highlight conditional independence relationships between the sample variables. We first formulate a convex relaxation of this combinatorial problem, we then detail two efficient first-order algorithms with low memory requirements to solve large-scale, dense problem instances.