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Group Symmetry and Covariance Regularization

Shah, Parikshit and Chandrasekaran, Venkat (2012) Group Symmetry and Covariance Regularization. Electronic Journal of Statistics, 6 . pp. 1600-1640. ISSN 1935-7524.

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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 on 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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Additional Information:© 2012 Institute of Mathematical Statistics. Received November 2011. The authors would like to thank Pablo Parrilo, Benjamin Recht, Alan Willsky, and Stephen Wright for helpful discussions.
Subject Keywords:Group invariance, covariance selection, exchange-ability, high dimensional asymptotics
Classification Code:AMS 2000 subject classifications: Primary 62F12, 62H12
Record Number:CaltechAUTHORS:20121004-134807001
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:34686
Deposited By: Tony Diaz
Deposited On:04 Oct 2012 22:18
Last Modified:03 Oct 2019 04:21

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