Sparse inverse covariance estimation with the graphical lasso

Biostatistics. 2008 Jul;9(3):432-41. doi: 10.1093/biostatistics/kxm045. Epub 2007 Dec 12.


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 ( approximately 500,000 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.

Publication types

  • Research Support, N.I.H., Extramural
  • Research Support, U.S. Gov't, Non-P.H.S.

MeSH terms

  • Algorithms
  • Animals
  • Biometry / methods
  • Data Interpretation, Statistical
  • Humans
  • Models, Statistical*
  • Neural Networks, Computer*
  • Proteomics / methods
  • Reference Values
  • Regression Analysis*
  • Sample Size
  • Signal Transduction
  • Time Factors