The stochastic block model (SBM) is one of the most widely used generative models for network data. Many continuous-time dynamic network models are built upon the same assumption as the SBM: edges or events between all pairs of nodes are conditionally independent given the block or community memberships, which prevents them from reproducing higher-order motifs such as triangles that are commonly observed in real networks. We propose the multivariate community Hawkes (MULCH) model, an extremely flexible community-based model for continuous-time networks that introduces dependence between node pairs using structured multivariate Hawkes processes. We fit the model using a spectral clustering and likelihood-based local refinement procedure. We find that our proposed MULCH model is far more accurate than existing models both for predictive and generative tasks.

翻译：随机区块模型(SBM)是网络数据最广泛使用的基因化模型之一,许多连续时间动态网络模型建立在与SBM相同的假设基础上:所有节点之间的边缘或事件由于区块或社区成员资格而有条件地独立,这使它们无法再生成在真实网络中常见的三角形等更高排序的分子。我们提议多变量社区鹰模型(MULCH)模型,这是一个非常灵活的社区连续时间网络模型,它通过结构化多变量鹰进程在节点对配之间产生依赖性。我们用光谱集群和基于可能性的本地改进程序来适应模型。我们发现,我们提议的MULCH模型比现有的预测性和基因化任务模型更准确。