B1091
Title: Group network Hawkes process
Authors: Guanhua Fang - Columbia University (United States)
Haochen Xu - Fudan University (China)
Xuening Zhu - Fudan University (China)
Yongtao Guan - University of Miami (United States)
Ganggang Xu - University of Miami (United States) [presenting]
Abstract: The event occurrences of individuals interacting in a network are studied. To characterize the dynamic interactions among the individuals, we propose a group network Hawkes process (GNHP) model whose network structure is observed and fixed. In particular, we introduce a latent group structure among individuals to account for the heterogeneous user-specific characteristics. A maximum likelihood approach is proposed to cluster individuals in the network and estimate model parameters simultaneously. A fast EM algorithm is subsequently developed by utilizing the branching representation of the proposed GNHP model. Theoretical properties of the resulting estimators of group memberships and model parameters are investigated under both settings when the number of latent groups $G$ is over-specified or correctly specified. A data-driven criterion that can consistently identify the true $G$ under mild conditions is derived. Extensive simulation studies and an application to a data set collected from Sina Weibo are used to illustrate the effectiveness of the proposed methodology.
