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.
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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 -