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.
Keywords
Lasso (programming language)CovarianceCoordinate descentInverseEstimation of covariance matricesAlgorithmComputer scienceSimple (philosophy)Graphical modelCovariance matrixInverse problemMathematical optimizationGradient descentMatrix (chemical analysis)MathematicsApplied mathematicsArtificial intelligenceStatisticsArtificial neural network
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Publication Info
- Year
- 2007
- Type
- article
- Volume
- 9
- Issue
- 3
- Pages
- 432-441
- Citations
- 6237
- Access
- Closed
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Cite This
Jerome H. Friedman,
Trevor Hastie,
Robert Tibshirani
(2007).
Sparse inverse covariance estimation with the graphical lasso.
Biostatistics
, 9
(3)
, 432-441.
https://doi.org/10.1093/biostatistics/kxm045
Identifiers
- DOI
- 10.1093/biostatistics/kxm045