Open Access
December 2017 Structural similarity and difference testing on multiple sparse Gaussian graphical models
Weidong Liu
Ann. Statist. 45(6): 2680-2707 (December 2017). DOI: 10.1214/17-AOS1539


We present a new framework on inferring structural similarities and differences among multiple high-dimensional Gaussian graphical models (GGMs) corresponding to the same set of variables under distinct experimental conditions. The new framework adopts the partial correlation coefficients to characterize the potential changes of dependency strengths between two variables. A hierarchical method has been further developed to recover edges with different or similar dependency strengths across multiple GGMs. In particular, we first construct two-sample test statistics for testing the equality of partial correlation coefficients and conduct large-scale multiple tests to estimate the substructure of differential dependencies. After removing differential substructure from original GGMs, a follow-up multiple testing procedure is used to detect the substructure of similar dependencies among GGMs. In each step, false discovery rate is controlled asymptotically at a desired level. Power results are proved, which demonstrate that our method is more powerful on finding common edges than the common approach that separately estimates GGMs. The performance of the proposed hierarchical method is illustrated on simulated datasets.


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Weidong Liu. "Structural similarity and difference testing on multiple sparse Gaussian graphical models." Ann. Statist. 45 (6) 2680 - 2707, December 2017.


Received: 1 February 2016; Revised: 1 January 2017; Published: December 2017
First available in Project Euclid: 15 December 2017

zbMATH: 06838147
MathSciNet: MR3737906
Digital Object Identifier: 10.1214/17-AOS1539

Primary: 62H12 , 62H15

Keywords: Common substructure , False discovery rate , Gaussian graphical model , high dimensional , structural difference , structural similarity

Rights: Copyright © 2017 Institute of Mathematical Statistics

Vol.45 • No. 6 • December 2017
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