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Title: Statistical inference for networks of high-dimensional point processes Authors:  Ali Shojaie - University of Washington (United States) [presenting]
Abstract: Fueled in part by recent applications in neuroscience, high-dimensional Hawkes process has become a popular tool for modeling the network of interactions among multivariate point process data. While evaluating the uncertainty of the network estimates is critical in scientific applications, existing methodological and theoretical work has primarily focused on estimation. To bridge this gap, we develop a new statistical inference procedure for high-dimensional multivariate Hawkes processes. The key ingredient to this inference procedure is a new concentration inequality on the first- and second-order statistics for integrated stochastic processes, which summarizes the entire history of the process. Combining recent results on martingale central limit theory with the new concentration inequality, we can characterize the convergence rate of the test statistics. We investigate finite sample properties of our inferential tools using extensive simulation studies and demonstrate their utility in an application to a neuron spike train data.