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.

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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

Tags

Communities of Interest

  • Autonomy

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Computational Complexity
  • Computer Science
  • Convergence
  • Covariance
  • Data Science
  • Electrical Engineering
  • Estimators
  • Information Science
  • Mathematical Analysis
  • Signal Processing
  • Simulations
  • Standards
  • Statistical Algorithms
  • Statistical Analysis
  • Statistics

Fields of Study

  • Computer science

Readers

  • Microwave Engineering.
  • Neural Network Machine Learning.
  • Statistical inference.