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Title: An omnibus embedding for multiple random graphs, and applications to multiscale joint network inference Authors:  Avanti Athreya - Johns Hopkins University (United States) [presenting]
Abstract: Principled, scalable methods for statistical inference across multiple graphs is of vital importance in a host of application domains. We describe an omnibus embedding in which multiple graphs on the same vertex set are jointly embedded into a single space with a distinct representation for each graph. We prove a central limit theorem for this omnibus embedding, and we show that this simultaneous embedding into a single common space allows for the comparison of graphs without further orthogonal alignments. Moreover, the existence of multiple embedded points for each vertex renders possible the resolution of important multiscale graph inference goals, such as the identification of specific subgraphs or vertices as drivers of similarity or difference across large networks. We demonstrate the utility of the omnibus embedding in two analyses of connectomic graphs generated from MRI scans of the brain in human subjects. We show how the omnibus embedding can be used to detect statistically significant differences, at multiple scales, across these networks, with an identification of specific brain regions that are associated with population-level differences and which may be loci of markers of pathology.