Sketched covariance testing: A compression-statistics tradeoff

Gautam Dasarathy, Parikshit Shah, Richard G. Baraniuk

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

1 Citation (Scopus)

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 publication2017 IEEE International Symposium on Information Theory, ISIT 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2268-2272
Number of pages5
ISBN (Electronic)9781509040964
DOIs
StatePublished - Aug 9 2017
Externally publishedYes
Event2017 IEEE International Symposium on Information Theory, ISIT 2017 - Aachen, Germany
Duration: Jun 25 2017Jun 30 2017

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095

Other

Other2017 IEEE International Symposium on Information Theory, ISIT 2017
CountryGermany
CityAachen
Period6/25/176/30/17

Fingerprint

Compression
Trade-offs
Statistics
Hypothesis Testing
Covariance matrix
Testing
Biquadrate
Sketching
Statistical tests
Multivariate Analysis
Statistical test
Quantify
Framework

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics

Cite this

Dasarathy, G., Shah, P., & Baraniuk, R. G. (2017). Sketched covariance testing: A compression-statistics tradeoff. In 2017 IEEE International Symposium on Information Theory, ISIT 2017 (pp. 2268-2272). [8006933] (IEEE International Symposium on Information Theory - Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2017.8006933

Sketched covariance testing : A compression-statistics tradeoff. / Dasarathy, Gautam; Shah, Parikshit; Baraniuk, Richard G.

2017 IEEE International Symposium on Information Theory, ISIT 2017. Institute of Electrical and Electronics Engineers Inc., 2017. p. 2268-2272 8006933 (IEEE International Symposium on Information Theory - Proceedings).

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

Dasarathy, G, Shah, P & Baraniuk, RG 2017, Sketched covariance testing: A compression-statistics tradeoff. in 2017 IEEE International Symposium on Information Theory, ISIT 2017., 8006933, IEEE International Symposium on Information Theory - Proceedings, Institute of Electrical and Electronics Engineers Inc., pp. 2268-2272, 2017 IEEE International Symposium on Information Theory, ISIT 2017, Aachen, Germany, 6/25/17. https://doi.org/10.1109/ISIT.2017.8006933
Dasarathy G, Shah P, Baraniuk RG. Sketched covariance testing: A compression-statistics tradeoff. In 2017 IEEE International Symposium on Information Theory, ISIT 2017. Institute of Electrical and Electronics Engineers Inc. 2017. p. 2268-2272. 8006933. (IEEE International Symposium on Information Theory - Proceedings). https://doi.org/10.1109/ISIT.2017.8006933
Dasarathy, Gautam ; Shah, Parikshit ; Baraniuk, Richard G. / Sketched covariance testing : A compression-statistics tradeoff. 2017 IEEE International Symposium on Information Theory, ISIT 2017. Institute of Electrical and Electronics Engineers Inc., 2017. pp. 2268-2272 (IEEE International Symposium on Information Theory - Proceedings).
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