时间网络的依赖社区Hawkes过程模型的谱聚类
Spectral clustering for dependent community Hawkes process models of temporal networks
AI总结：
针对时间网络中的社区结构与节点对依赖性，提出依赖社区Hawkes（DCH）模型，结合随机块模型与相互激发Hawkes过程，推导了谱聚类误聚类误差的非渐近上界，并提出基于广义矩估计的高可扩展参数估计方法。
摘要：
通过带有时间戳的关系事件数据在连续时间内观察到的时间网络，常见于在线社交媒体通信、金融交易和国际关系等应用场景中。时间网络通常表现出社区结构和节点对之间的强依赖模式。这种依赖可以通过相互激发来建模，即从发送方到接收方节点的交互事件会增加其他节点对之间未来事件发生的可能性。我们为一类我们称之为依赖社区Hawkes（DCH）模型的模型提供了统计结果，该模型结合了随机块模型和相互激发的Hawkes过程，分别用于建模社区结构和节点对之间的依赖关系。我们推导出了事件计数矩阵上谱聚类的误聚类误差的非渐近上界，该上界是节点数和社区数、持续时间以及模型中依赖量的函数。我们的结果利用了关于界定多元Hawkes过程计数向量与高斯向量之间适当距离的最新结果，以及随机矩阵理论的结果。我们还提出了一种仅包含自激发和互激发的DCH模型，以及使用广义矩估计（GMM）估计器的高可扩展参数估计，我们证明了该估计器对于不断增长的网络规模和持续时间是一致的。
英文摘要：
Temporal networks observed continuously over time through timestamped relational events data are commonly encountered in application settings including online social media communications, financial transactions, and international relations. Temporal networks often exhibit community structure and strong dependence patterns among node pairs. This dependence can be modeled through mutual excitations, where an interaction event from a sender to a receiver node increases the possibility of future events among other node pairs. We provide statistical results for a class of models that we call dependent community Hawkes (DCH) models, which combine the stochastic block model with mutually exciting Hawkes processes for modeling both community structure and dependence among node pairs, respectively. We derive a non-asymptotic upper bound on the misclustering error of spectral clustering on the event count matrix as a function of the number of nodes and communities, time duration, and the amount of dependence in the model. Our result leverages recent results on bounding an appropriate distance between a multivariate Hawkes process count vector and a Gaussian vector, along with results from random matrix theory. We also propose a DCH model that incorporates only self and reciprocal excitation along with highly scalable parameter estimation using a Generalized Method of Moments (GMM) estimator that we demonstrate to be consistent for growing network size and time duration.
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