Learning Latent Network Structure from High-Dimensional Multivariate Point Processes

• Activity Number: 80 - Graphical Models and Causal Inference
• Type: Contributed
• Date/Time: Sunday, July 28, 2019 : 4:00 PM to 5:50 PM
• 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; likelihood ratio test; model selection consistency; non-asymptotic error bound; nonstationary

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 flexible class of nonstationary and nonlinear Hawkes processes that allow both excitatory and inhibitory effects. Using a thinning representation, we establish concentration inequalities for the first and second order statistics of the proposed Hawkes process. We estimate the latent network structure using an efficient sparse least squares estimation approach, and establish the non-asymptotic error bound and selection consistency of the nonparametric estimator. Furthermore, we describe a penalized estimation based statistic to test for the stationarity of the underlying processes. Our theoretical results are corroborated by simulation studies and an application to a neuron spike train dataset.