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Latent Network Structure Learning From High-Dimensional Multivariate Point Processes

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Version 2 2022-09-07, 18:40
Version 1 2022-07-15, 15:20
journal contribution
posted on 2022-09-07, 18:40 authored by Biao Cai, Jingfei Zhang, Yongtao Guan

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 dataset. Supplementary materials for this article are available online.

Funding

Zhang’s research is supported by NSF DMS-2015190 and Guan’s research is supported by NSF DMS-1810591.

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