Activity Number:
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286
- Learning Networks from Point Processes: Neuronal Connectivity Networks and Beyond
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Type:
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Invited
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Date/Time:
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Wednesday, August 5, 2020 : 10:00 AM to 11:50 AM
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Sponsor:
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Section on Statistical Learning and Data Science
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Abstract #308133
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Title:
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Latent Network Structure Learning from High-Dimensional Multivariate Point Processes
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Author(s):
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Biao Cai and Emma Jingfei Zhang* and Yongtao Guan
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Companies:
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University of Miami and University of Miami and University of Miami
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Keywords:
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Hawkes process;
non-asymptotic error bound;
nonlinear;
nonstationarity;
selection consistency
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Abstract:
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Learning the latent network structure from large scale multivariate point process data is an important task in a wide range of scientific and business applications. For instance, we might wish to estimate the neuronal functional connectivity network based on spiking (or firing) times recorded from a collection of neurons. To characterize the complex processes underlying the observed point patterns, we propose a new and flexible class of non-linear and non-stationary Hawkes processes that allow both excitatory and inhibitory effects. We estimate the latent network structure using a scalable sparse least squares estimation approach. Using a thinning representation, we establish concentration inequalities for the first and second order statistics of the proposed class of Hawkes processes. Such theoretical results enable us to establish the non-asymptotic error bound and the selection consistency of the estimated parameters. Furthermore, we describe a penalized least squares based statistic for testing if the background intensity is constant in time. We apply our proposed method to a neurophysiological data set that studies working memory.
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Authors who are presenting talks have a * after their name.