Latent Network Structure Learning from High Dimensional Multivariate Point Processes

• URL: http://arxiv.org/abs/2004.03569v2
• Date: Tue, 19 Jan 2021 20:07:22 GMT
• Title: Latent Network Structure Learning from High Dimensional Multivariate Point Processes
• Authors: Biao Cai, Jingfei Zhang, Yongtao Guan
• Abstract summary: We propose a new class of nonstationary Hawkes processes to characterize the complex processes underlying the observed data. We estimate the latent network structure using an efficient sparse least squares estimation approach. We demonstrate the efficacy of our proposed method through simulation studies and an application to a neuron spike train data set.
• Score: 5.079425170410857
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 times recorded from a collection of neurons. To characterize the complex processes underlying the observed data, we propose a new and flexible class of nonstationary Hawkes processes that allow both excitatory and inhibitory effects. We estimate the latent network structure using an efficient sparse least squares estimation approach. Using a thinning representation, we establish concentration inequalities for the first and second order statistics of the proposed Hawkes process. Such theoretical results enable us to establish the non-asymptotic error bound and the selection consistency of the estimated parameters. Furthermore, we describe a least squares loss based statistic for testing if the background intensity is constant in time. We demonstrate the efficacy of our proposed method through simulation studies and an application to a neuron spike train data set.

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