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 Meinshausen and Bühlmann (2006). We illustrate the method on some cell-signaling data from proteomics.
%0 Journal Article
%1 friedman_sparse_2008
%A Friedman, Jerome
%A Hastie, Trevor
%A Tibshirani, Robert
%D 2008
%J Biostatistics
%K L1, Lasso, covariance graph matrices matrix, regularization, sparse theory,
%N 3
%P 432--441
%R 10.1093/biostatistics/kxm045
%T Sparse inverse covariance estimation with the graphical lasso
%U http://biostatistics.oxfordjournals.org/content/9/3/432
%V 9
%X 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 Meinshausen and Bühlmann (2006). We illustrate the method on some cell-signaling data from proteomics.
@article{friedman_sparse_2008,
abstract = {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 Meinshausen and Bühlmann (2006). We illustrate the method on some cell-signaling data from proteomics.},
added-at = {2017-01-09T13:57:26.000+0100},
author = {Friedman, Jerome and Hastie, Trevor and Tibshirani, Robert},
biburl = {https://www.bibsonomy.org/bibtex/2489dda20b5e59611f836530f90e65a55/yourwelcome},
doi = {10.1093/biostatistics/kxm045},
interhash = {1b78d59988c38393424053ca68ce8c91},
intrahash = {489dda20b5e59611f836530f90e65a55},
issn = {1465-4644, 1468-4357},
journal = {Biostatistics},
keywords = {L1, Lasso, covariance graph matrices matrix, regularization, sparse theory,},
language = {en},
month = jul,
number = 3,
pages = {432--441},
timestamp = {2017-01-09T14:01:11.000+0100},
title = {Sparse inverse covariance estimation with the graphical lasso},
url = {http://biostatistics.oxfordjournals.org/content/9/3/432},
urldate = {2013-03-15},
volume = 9,
year = 2008
}