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Abstract:
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Many data sets from across the sciences collect sequences of matrix- and tensor-structured data; we refer to such data as tensor time series. We are particularly motivated by electrophysiology studies in which electrical activity at multiple locations in the brain is measured over time. There is a pressing need in this application area to obtain flexible stochastic models of dynamic changes in neural subnetworks over time, with such models serving as an important starting point for analyses incorporating variation across study subjects and association with traits of the subjects and behavior. We propose a flexible class of Bayesian dynamic tensor factor models, which reduce dimensionality and maintain interpretability through the incorporation of sparsity constraints. Starting with a stochastic differential equation (SDE) representation, we define an efficient MCMC algorithm for posterior computation using a simulation smoother. The ability to accurately infer dynamically changing subnetworks is shown through simulations, and the methods are applied to mouse electrophysiology data.
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