DOI: 10.1093/biostatistics/kxm045. Sparse inverse covariance estimation with the graphical lasso

Sparse inverse covariance estimation with the graphical lasso

10.1093/biostatistics/kxm045

Crossref journal-article

Oxford University Press (OUP)

Biostatistics (286)

Abstract

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.

Bibliography

Friedman, J., Hastie, T., & Tibshirani, R. (2007). Sparse inverse covariance estimation with the graphical lasso. Biostatistics, 9(3), 432â441.

Authors 3

Jerome Friedman (first)
Trevor Hastie (additional)
Robert Tibshirani (additional)

References 9 Referenced 4,319

{'key': '2024032313142317100_bib1', 'article-title': 'Model selection through sparse maximum likelihood estimation', 'author': 'Banerjee', 'year': '2007', 'journal-title': 'Journal of Machine Learning Research'} / Journal of Machine Learning Research / Model selection through sparse maximum likelihood estimation by Banerjee (2007)
10.1017/CBO9780511804441 / Convex Optimization by Boyd (2004)
{'key': '2024032313142317100_bib3', 'article-title': 'Covariance selection for non-chordal graphs via chordal embedding', 'author': 'Dahl', 'year': '2007', 'journal-title': 'Optimization Methods and Software (to appear)'} / Optimization Methods and Software (to appear) / Covariance selection for non-chordal graphs via chordal embedding by Dahl (2007)
{'key': '2024032313142317100_bib4', 'article-title': 'Pathwise coordinate optimization', 'volume': '2', 'author': 'Friedman', 'year': '2007', 'journal-title': 'Annals of Applied Statistics'} / Annals of Applied Statistics / Pathwise coordinate optimization by Friedman (2007)
10.1214/009053606000000281 / Annals of Statistics / High dimensional graphs and variable selection with the lasso by Meinshausen (2006)
10.1126/science.1105809 / Science / Causal protein-signaling networks derived from multiparameter single-cell data by Sachs (2003)
10.1137/S0895479896303430 / SIAM Journal on Matrix Analysis and Applications / Determinant maximization with linear matrix inequality constraints by Vandenberghe (1998)
{'key': '2024032313142317100_bib8', 'article-title': 'Coordinate descent procedures for lasso penalized regression', 'volume': '3', 'author': 'Wu', 'year': '2007', 'journal-title': 'Annals of Applied Statistics'} / Annals of Applied Statistics / Coordinate descent procedures for lasso penalized regression by Wu (2007)
10.1093/biomet/asm018 / Biometrika / Model selection and estimation in the gaussian graphical model by Yuan (2007)

Dates

Type	When
Created	17 years, 8 months ago (Dec. 13, 2007, 8:13 p.m.)
Deposited	1 year, 5 months ago (March 23, 2024, 9:14 a.m.)
Indexed	9 minutes ago (Aug. 29, 2025, 3:45 p.m.)
Issued	17 years, 8 months ago (Dec. 12, 2007)
Published	17 years, 8 months ago (Dec. 12, 2007)
Published Online	17 years, 8 months ago (Dec. 12, 2007)
Published Print	17 years, 1 month ago (July 1, 2008)

Funders 0

None

BibTeX

@article{Friedman_2007, title={Sparse inverse covariance estimation with the graphical lasso}, volume={9}, ISSN={1465-4644}, url={http://dx.doi.org/10.1093/biostatistics/kxm045}, DOI={10.1093/biostatistics/kxm045}, number={3}, journal={Biostatistics}, publisher={Oxford University Press (OUP)}, author={Friedman, Jerome and Hastie, Trevor and Tibshirani, Robert}, year={2007}, month=dec, pages={432–441} }

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