Estimating high-dimensional covariance matrices with misses for Kronecker product expansion models

Mahdi Zamanighomi, Zhengdao Wang, Georgios B. Giannakis

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

We study the problem of high-dimensional covariance matrix estimation from partial observations. We consider covariance matrices modeled as Kronecker products of matrix factors, and rely on observations with missing values. In the absence of missing data, observation vectors are assumed to be i.i.d multivariate Gaussian. In particular, we propose a new procedure computationally affordable in high dimension to extend an existing permuted rank-penalized least-squares method to the case of missing data. Our approach is applicable to a large variety of missing data mechanisms, whether the process generating missing values is random or not, and does not require imputation techniques. We introduce a novel unbiased estimator and characterize its convergence rate to the true covariance matrix measured by the spectral norm of a permutation operator. We establish a tight outer bound on the square error of our estimate, and elucidate consequences of missing values on the estimation performance. Different schemes are compared by numerical simulations in order to test our proposed estimator.

Original languageEnglish (US)
Title of host publication2016 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2667-2671
Number of pages5
ISBN (Electronic)9781479999880
DOIs
StatePublished - May 18 2016
Event41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016 - Shanghai, China
Duration: Mar 20 2016Mar 25 2016

Publication series

NameICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings
Volume2016-May
ISSN (Print)1520-6149

Other

Other41st IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP 2016
CountryChina
CityShanghai
Period3/20/163/25/16

Keywords

  • Kronecker product
  • covariance matrices
  • high-dimensional
  • missing data

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