%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 }