Accession Number

ADA581712

Title

Kronecker Graphical Lasso.

Publication Date

Aug 2012

Media Count

5p

Personal Author

I. A. Hero S. Zhou T. Tsiligkaridis

Abstract

We consider highdimensional estimation of a (possibly sparse) Kroneckerdecomposable covariance matrix given i.i.d. Gaussian samples. We propose a sparse covariance estimation algorithm, the Kronecker Graphical Lasso (KGlasso), for the highdimensional setting that takes advantage of structure and sparsity. Convergence and limit point characterization of this iterative algorithm are established. Compared to standard Glasso, KGlasso has low computational complexity as the dimension of the covariance matrix increases. We derive a tight mean squared error (MSE) convergence rate for KGlasso and show that it outperforms standard Glasso and the flipflop algorithm. Simulations validate these results and show that KGlasso outperforms the maximumlikelihood solution (FF) in the highdimensional smallsample regime.

Keywords

Algorithms Computerized simulation Consistency Convergence Covariance Covariance matrix Estimates Flipflop algorithm Highdimensional consistency Kronecker graphical lasso L1penalized maximum likelihood estimators Learning machines Matrices(Mathematics) Maximum likelihood estimation Monte carlo method Multivariate gaussian models Signal processing Sparse covariance estimation algorithms Standard graphical lasso algorithm Structured covariance estimation Symposia


Source Agency

Non Paid ADAS

NTIS Subject Category

72B  Algebra, Analysis, Geometry, & Mathematical Logic 72F  Statistical Analysis 62  Computers, Control & Information Theory

Corporate Author

Michigan Univ., Ann Arbor. Dept. of Electrical Engineering and Computer Science.

Document Type

Technical report

Title Note

Conference paper.

NTIS Issue Number

1325

Contract Number

W911NF1110391
