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 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.

翻译：本研究探究个体在网络中进行交互时的事件发生模式。为刻画个体间的动态交互特性，我们提出一种网络结构已知且固定的群组网络霍克斯过程模型。该模型特别引入个体间的潜在群组结构，用于解释异质性用户特征。我们提出极大似然方法，同步实现网络中的个体聚类与模型参数估计。基于所提出的群组网络霍克斯过程模型的分支表示，进一步开发了快速期望最大化算法。在潜在群组数量$G$被过度指定或正确指定的两种情境下，研究了群组成员身份与模型参数的估计量理论性质。推导出在温和条件下可一致识别真实$G$的数据驱动准则。通过大量模拟实验及新浪微博数据集的应用，验证了所提方法的有效性。