具有依赖边和层的社区检测多层概率网络模型
A Multilayer Probit Network Model for Community Detection with Dependent Edges and Layers
AI总结：
本文提出一种多层概率网络模型，用于考虑层间和层内依赖结构的社区检测方法，结合随机块模型和多元概率模型，通过约束似然方法和高效算法实现参数估计和社区检测。
摘要：
在多层网络中进行社区检测，其目标是识别出在多个网络层中表现出相似连接模式的节点群体，近年来受到了广泛关注。大多数现有方法都基于不同层之间要么独立要么遵循特定依赖结构的假设，且同一层内的边是独立的。在本文中，我们提出了一种新的多层网络社区检测方法，能够考虑广泛存在的层间和层内依赖结构。所提出的方法将多层随机块模型与多元概率模型相结合，以捕捉层间依赖的结构，同时也允许层内依赖。为了便于参数估计，我们开发了一种约束成对似然方法，并结合了高效的交替更新算法。还建立了所提出方法的渐近性质，重点考察层间和层内依赖对参数估计和社区检测准确性的影响。理论结果通过在模拟网络和现实世界多层贸易网络上的大量数值实验得到支持。
英文摘要：
Community detection in multilayer networks, which aims to identify groups of nodes exhibiting similar connectivity patterns across multiple network layers, has attracted considerable attention in recent years. Most existing methods are based on the assumption that different layers are either independent or follow specific dependence structures, and edges within the same layer are independent. In this article, we propose a novel method for community detection in multilayer networks that accounts for a broad range of inter-layer and intra-layer dependence structures. The proposed method integrates the multilayer stochastic block model for community detection with a multivariate probit model to capture the structures of inter-layer dependence, which also allows intra-layer dependence. To facilitate parameter estimation, we develop a constrained pairwise likelihood method coupled with an efficient alternating updating algorithm. The asymptotic properties of the proposed method are also established, with a focus on examining the influence of inter-layer and intra-layer dependences on the accuracy of both parameter estimation and community detection. The theoretical results are supported by extensive numerical experiments on both simulated networks and a real-world multilayer trade network.
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