TY - GEN

T1 - Sketched covariance testing

T2 - 2017 IEEE International Symposium on Information Theory, ISIT 2017

AU - Dasarathy, Gautam

AU - Shah, Parikshit

AU - Baraniuk, Richard G.

PY - 2017/8/9

Y1 - 2017/8/9

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85034039775&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85034039775&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2017.8006933

DO - 10.1109/ISIT.2017.8006933

M3 - Conference contribution

AN - SCOPUS:85034039775

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 2268

EP - 2272

BT - 2017 IEEE International Symposium on Information Theory, ISIT 2017

PB - Institute of Electrical and Electronics Engineers Inc.

Y2 - 25 June 2017 through 30 June 2017

ER -