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Zbl 1143.62076
Friedman, Jerome; Hastie, Trevor; Tibshirani, Robert
Sparse inverse covariance estimation with the graphical lasso. (English)
[J] Biostatistics 9, No. 3, 432-441 (2008). ISSN 1465-4644; ISSN 1468-4357/e

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

MSC 2000:: *62P10 Appl. of statistics to biology
65C60 Computational problems in statistics
05C90 Appl. of graph theory

Keywords: Gaussian covariance; graphical model; L1

Citations: Zbl 1113.62082

Cited in: Zbl 1206.90115 Zbl 1179.90257 Zbl 1166.62040

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