  In this work, we consider hypothesis testing and anomaly detection on
datasets where each observation is a weighted network. Examples of such data
include brain connectivity networks from fMRI flow data, or word co-occurrence
counts for populations of individuals. Current approaches to hypothesis testing
for weighted networks typically requires thresholding the edge-weights, to
transform the data to binary networks. This results in a loss of information,
and outcomes are sensitivity to choice of threshold levels. Our work avoids
this, and we consider weighted-graph observations in two situations, 1) where
each graph belongs to one of two populations, and 2) where entities belong to
one of two populations, with each entity possessing multiple graphs (indexed
e.g. by time). Specifically, we propose a hierarchical Bayesian hypothesis
testing framework that models each population with a mixture of latent space
models for weighted networks, and then tests populations of networks for
differences in distribution over components. Our framework is capable of
population-level, entity-specific, as well as edge-specific hypothesis testing.
We apply it to synthetic data and three real-world datasets: two social media
datasets involving word co-occurrences from discussions on Twitter of the
political unrest in Brazil, and on Instagram concerning Attention Deficit
Hyperactivity Disorder (ADHD) and depression drugs, and one medical dataset
involving fMRI brain-scans of human subjects. The results show that our
proposed method has lower Type I error and higher statistical power compared to
alternatives that need to threshold the edge weights. Moreover, they show our
proposed method is better suited to deal with highly heterogeneous datasets.
