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Latent Network Structure Learning From High-Dimensional Multivariate Point Processes
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DOI：10.1080/01621459.2022.2102019.png)
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摘要
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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 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.
Keyword:
Multivariate Hawkes process
Non asymptotic error bound
Nonlinear Hawkes process
Nonstationary
Selection consistency
期刊
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IF:
3
论文数:
5.2K
被引数:
4.8W
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