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 (more or less 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 Bühlmann (2006).We illustrate the method on some cell-signaling data from proteomics.