Title :
Group symmetry and covariance regularization
Author :
Shah, Parikshit ; Chandrasekaran, Venkat
Author_Institution :
Univ. of Wisconsin at Madison, Madison, WI, USA
Abstract :
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.
Keywords :
computational complexity; convergence; covariance matrices; group theory; statistical analysis; convergence rates; covariance matrix regularization; group fixed point subspace; group invariance; group symmetry; statistical gains; statistical model; symmetric model; Biological system modeling; Complexity theory; Context; Convergence; Covariance matrix; Estimation; Orbits;
Conference_Titel :
Information Sciences and Systems (CISS), 2012 46th Annual Conference on
Conference_Location :
Princeton, NJ
Print_ISBN :
978-1-4673-3139-5
Electronic_ISBN :
978-1-4673-3138-8
DOI :
10.1109/CISS.2012.6310765