Summary: 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 (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 N. Meinshausen
and P. Bühlmann
[Ann. Stat. 34, No. 3, 1436–1462 (2006; Zbl 1113.62082
)]. We illustrate the method on some cell-signaling data from proteomics.