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2012 Group symmetry and covariance regularization
Parikshit Shah, Venkat Chandrasekaran
Electron. J. Statist. 6: 1600-1640 (2012). DOI: 10.1214/12-EJS723


Statistical models that possess symmetry arise in diverse settings such as random fields associated to geophysical phenomena, exchangeable processes in Bayesian statistics, and cyclostationary processes in engineering. We formalize the notion of a symmetric model via group invariance. We propose projection onto a group fixed point subspace as a fundamental way of regularizing covariance matrices in the high-dimensional regime. In terms of parameters associated to the group we derive precise rates of convergence of the regularized covariance matrix and demonstrate that significant statistical gains may be expected in terms of the sample complexity. We further explore the consequences of symmetry in related model-selection problems such as the learning of sparse covariance and inverse covariance matrices. We also verify our results with simulations.


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Parikshit Shah. Venkat Chandrasekaran. "Group symmetry and covariance regularization." Electron. J. Statist. 6 1600 - 1640, 2012.


Published: 2012
First available in Project Euclid: 26 September 2012

zbMATH: 1295.62023
MathSciNet: MR2988459
Digital Object Identifier: 10.1214/12-EJS723

Primary: 62F12 , 62H12

Keywords: covariance selection , exchangeability , group invariance , high dimensional asymptotics

Rights: Copyright © 2012 The Institute of Mathematical Statistics and the Bernoulli Society


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