Understanding both global and layer-specific group structures is useful for uncovering complex patterns in networks with multiple interaction types. In this work, we introduce a new model, the hierarchical multiplex stochastic blockmodel (HMPSBM), that simultaneously detects communities within individual layers of a multiplex network while inferring a global node clustering across the layers. A stochastic blockmodel is assumed in each layer, with probabilities of layer-level group memberships determined by a node's global group assignment. Our model uses a Bayesian framework, employing a probit stick-breaking process to construct node-specific mixing proportions over a set of shared Griffiths-Engen-McCloseky (GEM) distributions. These proportions determine layer-level community assignment, allowing for an unknown and varying number of groups across layers, while incorporating nodal covariate information to inform the global clustering. We propose a scalable variational inference procedure with parallelisable updates for application to large networks. Extensive simulation studies demonstrate our model's ability to accurately recover both global and layer-level clusters in complicated settings, and applications to real data showcase the model's effectiveness in uncovering interesting latent network structure.

翻译：理解网络的全局结构及各层特定群组结构，对于揭示具有多种交互类型网络中的复杂模式具有重要意义。本文提出一种新模型——层次化多重随机分块模型（HMPSBM），该模型能够在推断跨层全局节点聚类的同时，检测多重网络各独立层内的社区结构。我们在每一层假设随机分块模型，其中层级别群组成员概率由节点的全局群组分配决定。本模型采用贝叶斯框架，利用概率单位棒断过程在共享的格里菲斯-恩根-麦克克洛斯基（GEM）分布集合上构建节点特定的混合比例。这些比例决定了层级别社区分配，允许各层存在未知且可变的群组数量，同时纳入节点协变量信息以指导全局聚类。我们提出了一种可扩展的变分推断方法，其更新过程可并行化，适用于大型网络分析。大量仿真研究表明，本模型在复杂场景中能准确恢复全局及层级别聚类；实际数据应用则验证了该模型在揭示潜在网络结构方面的有效性。