Open Access
June 2012 High-dimensional structure estimation in Ising models: Local separation criterion
Animashree Anandkumar, Vincent Y. F. Tan, Furong Huang, Alan S. Willsky
Ann. Statist. 40(3): 1346-1375 (June 2012). DOI: 10.1214/12-AOS1009


We consider the problem of high-dimensional Ising (graphical) model selection. We propose a simple algorithm for structure estimation based on the thresholding of the empirical conditional variation distances. We introduce a novel criterion for tractable graph families, where this method is efficient, based on the presence of sparse local separators between node pairs in the underlying graph. For such graphs, the proposed algorithm has a sample complexity of $n=\Omega(J_{\min}^{-2}\log p)$, where $p$ is the number of variables, and $J_{\min}$ is the minimum (absolute) edge potential in the model. We also establish nonasymptotic necessary and sufficient conditions for structure estimation.


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Animashree Anandkumar. Vincent Y. F. Tan. Furong Huang. Alan S. Willsky. "High-dimensional structure estimation in Ising models: Local separation criterion." Ann. Statist. 40 (3) 1346 - 1375, June 2012.


Published: June 2012
First available in Project Euclid: 10 August 2012

zbMATH: 1297.62124
MathSciNet: MR3015028
Digital Object Identifier: 10.1214/12-AOS1009

Primary: 62H12
Secondary: 05C80

Keywords: graphical model selection , Ising models , local-separation property

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 3 • June 2012
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