Multi-level hypothesis testing for populations of heterogeneous networks

We consider hypothesis testing and anomaly detection on datasets where each observation is a weighted network. Current approaches to hypothesis testing for weighted networks typically require thresholding the edge-weights, to transform the data to binary networks. This results in a loss of information, and outcomes are sensitive 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). 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 two real-world datasets: a social media dataset involving word co-occurrences from discussions on Twitter of the political unrest in Brazil, and a medical dataset involving IMRI brain-scans of human subjects. The results show that our proposed method has lower Type-I error and higher statistical power compared to previous alternatives that need to threshold the edge weights.