3 research outputs found
Testing the Structure of a Gaussian Graphical Model with Reduced Transmissions in a Distributed Setting
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