Sparse inverse covariance estimation with the lasso

TL;DR

This paper introduces a fast algorithm for estimating sparse inverse covariance matrices using the lasso penalty, significantly outperforming existing methods and demonstrating practical application on proteomics data.

Contribution

It develops a simple, efficient coordinate descent algorithm for sparse inverse covariance estimation with the lasso, linking exact and approximate methods.

Findings

Algorithm solves large problems in about a minute

Significantly faster than competing methods (50-2000x)

Successfully applied to proteomics data

Abstract

We consider the problem of estimating sparse graphs by a lasso penalty applied to the inverse covariance matrix. Using a coordinate descent procedure for the lasso, we develop a simple algorithm that is remarkably fast: in the worst cases, it solves a 1000 node problem (~500,000 parameters) in about a minute, and is 50 to 2000 times faster than competing methods. It also provides a conceptual link between the exact problem and the approximation suggested by Meinhausen and Buhlmann (2006). We illustrate the method on some cell-signaling data from proteomics.