Pamfil A Roxana, Howison Sam D, Porter Mason A
Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom.
Department of Mathematics, University of California, Los Angeles, Los Angeles, California 90095, USA and Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom.
Phys Rev E. 2020 Dec;102(6-1):062307. doi: 10.1103/PhysRevE.102.062307.
Many recent developments in network analysis have focused on multilayer networks, which one can use to encode time-dependent interactions, multiple types of interactions, and other complications that arise in complex systems. Like their monolayer counterparts, multilayer networks in applications often have mesoscale features, such as community structure. A prominent approach for inferring such structures is the employment of multilayer stochastic block models (SBMs). A common (but potentially inadequate) assumption of these models is the sampling of edges in different layers independently, conditioned on the community labels of the nodes. In this paper, we relax this assumption of independence by incorporating edge correlations into an SBM-like model. We derive maximum-likelihood estimates of the key parameters of our model, and we propose a measure of layer correlation that reflects the similarity between the connectivity patterns in different layers. Finally, we explain how to use correlated models for edge "prediction" (i.e., inference) in multilayer networks. By incorporating edge correlations, we find that prediction accuracy improves both in synthetic networks and in a temporal network of shoppers who are connected to previously purchased grocery products.
网络分析领域最近的许多进展都集中在多层网络上，人们可以用它来编码随时间变化的相互作用、多种类型的相互作用以及复杂系统中出现的其他复杂情况。与单层网络类似，多层网络在应用中通常具有中尺度特征，比如社区结构。推断此类结构的一种突出方法是使用多层随机块模型（SBM）。这些模型一个常见（但可能不充分）的假设是，在节点社区标签的条件下，不同层的边独立抽样。在本文中，我们通过将边相关性纳入类似SBM的模型来放宽这种独立性假设。我们推导了模型关键参数的最大似然估计，并提出了一种层相关性度量，该度量反映了不同层中连通性模式之间的相似性。最后，我们解释了如何在多层网络中使用相关模型进行边的“预测”（即推理）。通过纳入边相关性，我们发现在合成网络以及与之前购买的杂货产品相关的购物者时间网络中，预测准确性都有所提高。
