First-order methods for sparse covariance selection

Alexandre d'Aspremont; Onureena Banerjee; Laurent El Ghaoui

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First-order methods for sparse covariance selection

Alexandre d'Aspremont·Onureena Banerjee·Laurent El Ghaoui

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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.

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Alexandre d'Aspremont, Onureena Banerjee, Laurent El Ghaoui. 2006-09-28. First-order methods for sparse covariance selection. https://arxiv.org/abs/math/0609812

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