Sparse inverse covariance estimation with the lasso

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.