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Activity Number: 168 - SLDS Student Paper Awards
Type: Topic Contributed
Date/Time: Tuesday, August 4, 2020 : 10:00 AM to 11:50 AM
Sponsor: Section on Statistical Learning and Data Science
Abstract #309766
Title: Statistical Inference for Networks of High-Dimensional Point Processes
Author(s): Xu Wang*
Keywords: Hawkes process; high dimensional inference; hypothesis testing; confidence intervals

Fueled in part by recent applications in neuroscience, high-dimensional Hawkes process have 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 have only focused on estimation. To bridge this gap, this paper proposes a high-dimensional statistical inference procedure with theoretical guarantees for multivariate Hawkes process. Key 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. We apply this concentration inequality, combining a recent result on martingale central limit theory, to give an upper bounds for the convergence rate of the test statistics. We verify our theoretical results with extensive simulation and an application to a neuron spike train data set.

Authors who are presenting talks have a * after their name.

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