Split Bregman Method for Sparse Inverse Covariance Estimation with Matrix Iteration Acceleration

TL;DR

This paper introduces a split Bregman method for sparse inverse covariance estimation that outperforms graphical lasso in speed and flexibility, enabling the use of various regularization terms beyond the  norm.

Contribution

The paper presents a novel split Bregman approach for sparse inverse covariance estimation, offering faster convergence and greater generality over existing methods like graphical lasso.

Findings

Significantly faster than graphical lasso on artificial and real data

Applicable to a broader class of regularization terms

Demonstrates improved efficiency and flexibility

Abstract

We consider the problem of estimating the inverse covariance matrix by maximizing the likelihood function with a penalty added to encourage the sparsity of the resulting matrix. We propose a new approach based on the split Bregman method to solve the regularized maximum likelihood estimation problem. We show that our method is significantly faster than the widely used graphical lasso method, which is based on blockwise coordinate descent, on both artificial and real-world data. More importantly, different from the graphical lasso, the split Bregman based method is much more general, and can be applied to a class of regularization terms other than the $\ell_1$ norm