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.
About the Speaker
Dr. Emma Jingfei Zhang is an assistant professor in the Department of Management Science at the Miami Herbert Business School, University of Miami. She graduated 2014 with a Ph.D. in statistics from the University of Illinois at Urbana-Champaign. Her work focuses on the statistical modeling and inference of network data, and temporal point processes. Her research combines computational statistics, dynamic processes and social science to exploit opportunities offered by large-scale datasets.