Sketched covariance testing: A compression-statistics tradeoff

Hypothesis testing of covariance matrices is an important problem in multivariate analysis. Given n data samples and a covariance matrix ∑ 0 , 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 test...

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Bibliographic Details
Main Authors: Dasarathy, Gautam, Shah, Parikshit, Baraniuk, Richard G.
Format: Conference Proceeding
Language:English
Subjects:
Complexity theory
Covariance matrices
Estimation
Proteins
Sparse matrices
Testing
Upper bound
Online Access:Request full text
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Summary:Hypothesis testing of covariance matrices is an important problem in multivariate analysis. Given n data samples and a covariance matrix ∑ 0 , 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.
ISSN:2576-2303
DOI:10.1109/ACSSC.2017.8335428