A0342
Title: Latent network structure learning from high-dimensional multivariate point processes
Authors: Emma Jingfei Zhang - Emory University (United States) [presenting]
Abstract: Learning the latent network structure from large-scale multivariate point process data is important in various scientific and business applications. For instance, it might be wished 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, a new and flexible class of nonstationary Hawkes processes is proposed that allow both excitatory and inhibitory effects. An efficient sparse least squares estimation approach estimates the latent network structure. Using a thinning representation, concentration inequalities are established 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, a least squares loss-based statistic is described for testing if the background intensity is constant in time. The efficacy of the proposed method through simulation studies and an application is demonstrated to a neuron spike train dataset.
