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| the Graphical Lasso| that is remarkably fast: it solves a 1000 node problem (» 500; 000 parameters) in at most a minute, and is 30 to 4000 times faster than competing methods. It also provides a conceptual link between the exact problem and the approximation suggested by Meinshausen & B˜ uhlmann (2006). We illustrate the method on some cell-signaling data from proteomics.