On the convexity in Kronecker structured covariance estimation

Ami Wiesel*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

5 Scopus citations

Abstract

A classical model for the covariance of a random matrix is the Kronecker product of two smaller covariance matrices associated with the rows and columns. Maximum likelihood estimation in such structures involves a non-convex optimization problem and is traditionally handled via an alternating maximization Flip-Flop technique. We prove that the problem is actually geodesically convex on the manifold of positive definite matrices. This allows for better analysis, efficient numerical solutions, and simple extensions through the use of additional geodesically convex regularizations. As an example, we propose to shrink the solution towards the identity when the number of samples is insufficient. We demonstrate the advantages of this approach using computer simulations.

Original languageEnglish
Title of host publication2012 IEEE Statistical Signal Processing Workshop, SSP 2012
Pages880-883
Number of pages4
DOIs
StatePublished - 2012
Event2012 IEEE Statistical Signal Processing Workshop, SSP 2012 - Ann Arbor, MI, United States
Duration: 5 Aug 20128 Aug 2012

Publication series

Name2012 IEEE Statistical Signal Processing Workshop, SSP 2012

Conference

Conference2012 IEEE Statistical Signal Processing Workshop, SSP 2012
Country/TerritoryUnited States
CityAnn Arbor, MI
Period5/08/128/08/12

Keywords

  • Geodesic convexity
  • Kronecker
  • covariance estimation
  • log-sum-exp

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