We propose a novel statistical model for sparse networks with overlapping community structure. The model is based on representing the graph as an exchangeable point process and naturally generalizes existing probabilistic models with overlapping block structure to the sparse regime. Our construction builds on vectors of completely random measures and has interpretable parameters, each node being assigned a vector representing its levels of affiliation to some latent communities. We develop methods for efficient simulation of this class of random graphs and for scalable posterior inference. We show that the approach proposed can recover interpretable structure of real world networks and can handle graphs with thousands of nodes and tens of thousands of edges.

中文翻译：

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社区重叠的稀疏和模块化图的可交换随机度量

我们为社区重叠的稀疏网络提出了一种新颖的统计模型。该模型基于将图表示为可交换点过程，并且自然地将具有重叠块结构的现有概率模型推广到稀疏状态。我们的构建基于完全随机度量的向量，并且具有可解释的参数，每个节点都被分配了一个向量，表示其与某些潜在社区的隶属关系。我们开发了用于此类随机图的高效仿真和可扩展后验推论的方法。我们表明，所提出的方法可以恢复现实世界网络的可解释结构，并且可以处理具有数千个节点和数万条边的图。