Sparse inverse covariance estimation with the graphical lasso.

@article{Friedman2008SparseIC,
  title={Sparse inverse covariance estimation with the graphical lasso.},
  author={J. Friedman and T. Hastie and R. Tibshirani},
  journal={Biostatistics},
  year={2008},
  volume={9 3},
  pages={
          432-41
        }
}
  • J. Friedman, T. Hastie, R. Tibshirani
  • Published 2008
  • Mathematics, Medicine
  • Biostatistics
  • 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 B… CONTINUE READING
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    References

    SHOWING 1-10 OF 15 REFERENCES
    Model Selection Through Sparse Maximum Likelihood Estimation
    • 161
    • Highly Influential
    High-dimensional graphs and variable selection with the Lasso
    • 2,901
    • Highly Influential
    • PDF
    Model selection and estimation in the Gaussian graphical model
    • 1,355
    • Highly Influential
    • PDF
    Covariance selection for nonchordal graphs via chordal embedding
    • 127
    • PDF
    PATHWISE COORDINATE OPTIMIZATION
    • 1,766
    • PDF
    Determinant Maximization with Linear Matrix Inequality Constraints
    • 676
    • PDF
    Convex Optimization
    • 35,952
    • PDF
    Causal Protein-Signaling Networks Derived from Multiparameter Single-Cell Data
    • 1,408
    • PDF
    Coordinate descent procedures for lasso penalized regression
    • Coordinate descent procedures for lasso penalized regression
    • 2007