Latent Network Structure Learning from High Dimensional Multivariate Point Processes (Emma Zhang - University of Miami)

Starts: 4:00 pm on Thursday, October 10, 2019
Ends: 5:00 pm on Thursday, October 10, 2019
Location: MCS B31, 111 Cummington Mall

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-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 novel 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 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. This is joint work with Biao Cai and Yongtao Guan.