Group Network Hawkes Process

• 成果类型: Article
• 署名作者: Fang, Guanhua; Xu, Ganggang; Xu, Haochen; Zhu, Xuening; Guan, Yongtao
• 署名单位: Fudan University; University of Miami; The Chinese University of Hong Kong, Shenzhen; Shenzhen Research Institute of Big Data; Fudan University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2023.2257889
• 发表日期: 2024
• 页码: 2328-2344
• 关键词: exciting point process; community detection; models

摘要

In this work, we study the event occurrences of individuals interacting in a network. 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 simultaneously cluster individuals in the network and estimate model parameters. A fast EM algorithm is subsequently developed by using 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 dataset collected from Sina Weibo are used to illustrate the effectiveness of the proposed methodology. Supplementary materials for this article are available online.