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B1236
Title: Euclidean mirrors and dynamics in network time series Authors:  Avanti Athreya - Johns Hopkins University (United States) [presenting]
Zachary Lubberts - University of Virginia (United States)
Youngser Park - Johns Hopkins University (United States)
Carey Priebe - Johns Hopkins University (United States)
Abstract: Understanding dramatic changes in the evolution of networks is central to statistical network inference. A joint network model is considered in which each node has an associated time-varying low-dimensional latent vector of feature data, and connection probabilities are functions of these vectors. Under mild assumptions, the time-varying evolution of the constellation of latent vectors exhibits a low-dimensional manifold structure under a suitable notion of distance. A measure of separation between the observed networks can approximate this distance. Euclidean representations exist for the underlying network structure, characterized by this distance, at any given time. These Euclidean representations and their data-driven estimates permit the visualization of network evolution and transform network inference questions such as change-point and anomaly detection into a classical setting. The methodology is illustrated with real and synthetic data, and change points are identified corresponding to key network shifts.