Sketched covariance testing: A compression-statistics tradeoff

Gautam Dasarathy, Parikshit Shah, Richard G. Baraniuk

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

Abstract

Hypothesis testing of covariance matrices is an important problem in multivariate analysis. Given n data samples and a covariance matrix Σ0, the goal is to determine whether or not the data is consistent with this matrix. In this paper we introduce a framework that we call sketched covariance testing, where the data is provided after being compressed by multiplying by a 'sketching' matrix A chosen by the analyst. We propose a statistical test in this setting and quantify an achievable sample complexity as a function of the amount of compression. Our result reveals an intriguing achievable tradeoff between the compression ratio and the statistical information required for reliable hypothesis testing; the sample complexity increases as the fourth power of the amount of compression.

Original languageEnglish (US)
Title of host publicationConference Record of 51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017
EditorsMichael B. Matthews
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages676-680
Number of pages5
ISBN (Electronic)9781538618233
DOIs
StatePublished - Apr 10 2018
Externally publishedYes
Event51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017 - Pacific Grove, United States
Duration: Oct 29 2017Nov 1 2017

Publication series

NameConference Record of 51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017
Volume2017-October

Other

Other51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017
CountryUnited States
CityPacific Grove
Period10/29/1711/1/17

ASJC Scopus subject areas

  • Control and Optimization
  • Computer Networks and Communications
  • Hardware and Architecture
  • Signal Processing
  • Biomedical Engineering
  • Instrumentation

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  • Cite this

    Dasarathy, G., Shah, P., & Baraniuk, R. G. (2018). Sketched covariance testing: A compression-statistics tradeoff. In M. B. Matthews (Ed.), Conference Record of 51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017 (pp. 676-680). (Conference Record of 51st Asilomar Conference on Signals, Systems and Computers, ACSSC 2017; Vol. 2017-October). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ACSSC.2017.8335428