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 ( approximately 500,000 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.
Friedman
Jerome
J
Department of Statistics, Stanford University, CA 94305, USA.
Hastie
Trevor
T
Tibshirani
Robert
R
D000465:Algorithms; D000818:Animals; D001699:Biometry / Q000379:methods; D003627:Data Interpretation, Statistical; D006801:Humans; D015233:Models, Statistical; D016571:Neural Networks, Computer; D040901:Proteomics / Q000379:methods; D012016:Reference Values; D012044:Regression Analysis; D018401:Sample Size; D015398:Signal Transduction; D013997:Time Factors