Latent Network Structure Learning from High-Dimensional Multivariate Point Processes

• Activity Number: 286 - Learning Networks from Point Processes: Neuronal Connectivity Networks and Beyond
• Type: Invited
• Date/Time: Wednesday, August 5, 2020 : 10:00 AM to 11:50 AM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Biao Cai and Emma Jingfei Zhang* and Yongtao Guan
• Companies: University of Miami and University of Miami and University of Miami
• Keywords: Hawkes process; non-asymptotic error bound; nonlinear; nonstationarity; selection consistency

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 (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.