Iterative Algorithm for Sparse Inverse Covariance Estimation

Although numerous algorithms have been proposed for solving this problem, this simple proximal gradient method is found to have attractive theoretical and numerical properties. G-ISTA has a linear rate of convergence, resulting in an O(log ε) iteration complexity to reach a tolerance of ε. This paper gives eigenvalue bounds for the G-ISTA iterates, providing a closed-form linear convergence rate. The rate is shown to be closely related to the condition number of the optimal point. Numerical convergence results and timing comparisons for the proposed method are presented. G-ISTA is shown to perform very well, especially when the optimal point is well-conditioned.