Testing the Structure of a Gaussian Graphical Model with Reduced Transmissions in a Distributed Setting

Abstract

Testing a covariance matrix following a Gaussian graphical model (GGM) is considered in this paper based on observations made at a set of distributed sensors grouped into clusters. Ordered transmissions are proposed to achieve the same Bayes risk as the optimum centralized energy unconstrained approach but with fewer transmissions and a completely distributed approach. In this approach, we represent the Bayes optimum test statistic as a sum of local test statistics which can be calculated by only utilizing the observations available at one cluster. We select one sensor to be the cluster head (CH) to collect and summarize the observed data in each cluster and intercluster communications are assumed to be inexpensive. The CHs with more informative observations transmit their data to the fusion center (FC) first. By halting before all transmissions have taken place, transmissions can be saved without performance loss. It is shown that this ordering approach can guarantee a lower bound on the average number of transmissions saved for any given GGM and the lower bound can approach approximately half the number of clusters when the minimum eigenvalue of the covariance matrix under the alternative hypothesis in each cluster becomes sufficiently large.

Department(s)

Electrical and Computer Engineering

Comments

This work was supported by the U.S. Army Research Laboratory and the U.S. Army Research Office under Grant W911NF-17-1-0331.

Keywords and Phrases

Covariance Matrix Testing; Distributed Detection; Energy Efficiency; Gaussian Graphical Models; Ordered Transmission

International Standard Serial Number (ISSN)

1053-587X

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2019 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Oct 2019

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