Kronecker Graphical Lasso
Abstract
We consider high-dimensional estimation of a (possibly sparse) Kronecker-decomposable covariance matrix given i.i.d. Gaussian samples. We propose a sparse covariance estimation algorithm, the Kronecker Graphical Lasso (KGlasso), for the high-dimensional 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 flip-flop algorithm. Simulations validate these results and show that KGlasso outperforms the maximum-likelihood solution (FF) in the high-dimensional small-sample regime.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 2012
- Accession Number
- ADA581712
Entities
People
- Alfred O. Hero III
- Shuheng Zhou
- Theodoros Tsiligkaridis
Organizations
- University of Michigan