Graphical lasso - Alchetron, The Free Social Encyclopedia

The graphical lasso is an algorithm to estimate the precision matrix (inverse of covariance matrix) from the observations from multivariate Gaussian distribution.

Setting

Consider observations X 1 , X 2 , . . . , X n from multivariate Gaussian distribution X ∼ N ( 0 , Σ ) . We are interested in estimating the precision matrix Θ = Σ − 1 .

The graphical lasso estimator is the Θ ^ such that:

Θ ^ = argmin Θ ≥ 0 ( tr ⁡ ( S Θ ) − log ⁡ det ( Θ ) + λ ∑ j ≠ k | Θ j k | )

Where S is the sample covariance, and λ is the penalizing parameter.

Application

To obtain the estimator in programs, users could use the R package glasso, or GraphLasso() function in Python Scikit-Learn package

References

Graphical lasso Wikipedia

(Text) CC BY-SA

Contents

Setting

Application

References