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April 2014 Gemini: Graph estimation with matrix variate normal instances
Shuheng Zhou
Ann. Statist. 42(2): 532-562 (April 2014). DOI: 10.1214/13-AOS1187


Undirected graphs can be used to describe matrix variate distributions. In this paper, we develop new methods for estimating the graphical structures and underlying parameters, namely, the row and column covariance and inverse covariance matrices from the matrix variate data. Under sparsity conditions, we show that one is able to recover the graphs and covariance matrices with a single random matrix from the matrix variate normal distribution. Our method extends, with suitable adaptation, to the general setting where replicates are available. We establish consistency and obtain the rates of convergence in the operator and the Frobenius norm. We show that having replicates will allow one to estimate more complicated graphical structures and achieve faster rates of convergence. We provide simulation evidence showing that we can recover graphical structures as well as estimating the precision matrices, as predicted by theory.


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Shuheng Zhou. "Gemini: Graph estimation with matrix variate normal instances." Ann. Statist. 42 (2) 532 - 562, April 2014.


Published: April 2014
First available in Project Euclid: 20 May 2014

zbMATH: 1301.62054
MathSciNet: MR3210978
Digital Object Identifier: 10.1214/13-AOS1187

Primary: 62F12
Secondary: 62F30

Keywords: Covariance estimation , graphical lasso , graphical model selection , inverse covariance estimation , matrix variate normal distribution

Rights: Copyright © 2014 Institute of Mathematical Statistics


Vol.42 • No. 2 • April 2014
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