论文标题
小组网络霍克斯进程
Group Network Hawkes Process
论文作者
论文摘要
在这项工作中，我们研究了在网络中相互作用的个人发生的事件。为了表征个体之间的动态相互作用，我们提出了一个组网络鹰队过程（GNHP）模型，该模型的网络结构被观察和固定。特别是，我们在个体之间介绍了一个潜在的群体结构，以说明异类用户特定的特征。提出了一种最大似然方法，以同时将个体聚集在网络中并估计模型参数。随后通过使用所提出的GNHP模型的分支表示形式来开发快速EM算法。在两个设置下，当潜在组的数量$ g $过度指定或正确指定时，研究了组成员资格和模型参数的理论属性。在轻度条件下，可以始终如一地识别真正的$ g $的数据驱动标准。大量的仿真研究和对从新南微博收集的数据集的应用用于说明所提出的方法的有效性。
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.
