Sparse inverse covariance estimation with the graphical 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 (similar to 500000 parameters) in at most a minute and is 30-4000 times faster than competing methods. It also provides a conceptual link between the exact problem and the approximation suggested by Meinshausen and Buhlmann (2006). We illustrate the method on some cell-signaling data from proteomics.