First-Order Methods for Sparse Covariance Selection

TITLE: First-Order Methods for Sparse Covariance Selection.

AUTHORS: Alexandre d'Aspremont, Onureena Banerjee, Laurent El Ghaoui

ABSTRACT: 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.

STATUS: SIAM Journal on Matrix Analysis and its Applications, 30(1), pp. 56-66, February 2008.

ArXiv PREPRINT: math.OC/0609812

PAPER: First-Order Methods for Sparse Covariance Selection in pdf