Multiplex networks have become increasingly more prevalent in many fields, and have emerged as a powerful tool for modeling the complexity of real networks. There is a critical need for developing inference models for multiplex networks that can take into account potential dependencies across different layers, particularly when the aim is community detection. We add to a limited literature by proposing a novel and efficient Bayesian model for community detection in multiplex networks. A key feature of our approach is the ability to model varying communities at different network layers. In contrast, many existing models assume the same communities for all layers. Moreover, our model automatically picks up the necessary number of communities at each layer (as validated by real data examples). This is appealing, since deciding the number of communities is a challenging aspect of community detection, and especially so in the multiplex setting, if one allows the communities to change across layers. Borrowing ideas from hierarchical Bayesian modeling, we use a hierarchical Dirichlet prior to model community labels across layers, allowing dependency in their structure. Given the community labels, a stochastic block model (SBM) is assumed for each layer. We develop an efficient slice sampler for sampling the posterior distribution of the community labels as well as the link probabilities between communities. In doing so, we address some unique challenges posed by coupling the complex likelihood of SBM with the hierarchical nature of the prior on the labels. An extensive empirical validation is performed on simulated and real data, demonstrating the superior performance of the model over single-layer alternatives, as well as the ability to uncover interesting structures in real networks.

翻译：多层网络在许多领域日益普及，并已成为建模真实网络复杂性的有力工具。当目标为社区检测时，亟需开发能考虑不同层间潜在依赖关系的多层网络推理模型。本文针对现有研究较少的领域提出了一种新颖且高效的贝叶斯模型，用于多层网络中的社区检测。该方法的关键特征在于能够建模不同网络层中变化的社区结构——相比之下，许多现有模型假设所有层共享相同的社区。此外，该模型能自动确定每层所需的社区数量（经真实数据示例验证）。这一特性颇具吸引力，因为社区数量确定本身是社区检测中的难题，在允许社区跨层变化的多层场景下更是如此。借鉴层次贝叶斯建模思想，我们采用层次狄利克雷先验来建模跨层的社区标签，允许其结构存在依赖关系。在给定社区标签的条件下，假设每层服从随机块模型（SBM）。我们开发了一种高效的切片采样器，用于对社区标签的后验分布以及社区间的连接概率进行采样。在此过程中，我们解决了将SBM的复杂似然函数与标签的层次先验耦合所带来的一系列独特挑战。通过在模拟数据与真实数据上进行广泛实证验证，结果表明该模型在性能上优于单层替代方法，并能揭示真实网络中蕴含的有趣结构。