标题： 检测随机块模型中的重复 motifs 和分层结构 显示英文标题

标题： Testing for Repeated Motifs and Hierarchical Structure in Stochastic Blockmodels

摘要： 神经科学、社交网络以及蛋白质-蛋白质相互作用网络中的网络数据复杂性不断增加，同时也有多个努力方向试图以不同尺度对这些数据进行建模和理解。 一种关键的多尺度网络建模技术假设网络具有分层结构，并通过将网络视为具有共享统计特性的多个层级划分，我们可以高效地发现复杂度可控的小型子图基元。 分层建模的一个例子是分层随机块模型（Hierarchical Stochastic Block Model），它旨在将复杂的网络建模为在整个网络中重复出现的社区结构。 引入重复结构允许在随机块模型（SBM）中跨社区进行参数绑定，与传统的块模型相比，可以降低模型复杂性。 在这项工作中，我们提出了一个框架来检验随机块模型框架下的重复主题分层结构。 我们描述了一个模型，该模型自然地将网络表示为一系列具有重复主题的子网络层次结构，并通过理论分析、广泛的模拟以及真实数据展示了检验的实际效用。 显示英文摘要

摘要： The rise in complexity of network data in neuroscience, social networks, and protein-protein interaction networks has been accompanied by several efforts to model and understand these data at different scales. A key multiscale network modeling technique posits hierarchical structure in the network, and by treating networks as multiple levels of subdivisions with shared statistical properties we can efficiently discover smaller subgraph primitives with manageable complexity. One such example of hierarchical modeling is the Hierarchical Stochastic Block Model, which seeks to model complex networks as being composed of community structures repeated across the network. Incorporating repeated structure allows for parameter tying across communities in the SBM, reducing the model complexity compared to the traditional blockmodel. In this work, we formulate a framework for testing for repeated motif hierarchical structure in the stochastic blockmodel framework. We describe a model which naturally expresses networks as a hierarchy of sub-networks with a set of motifs repeating across it, and we demonstrate the practical utility of the test through theoretical analysis and extensive simulation and real data.