Network Cluster-Robust Inference

Michael P. Leung
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引用次数: 6

Abstract

Since network data commonly consists of observations from a single large network, researchers often partition the network into clusters in order to apply cluster‐robust inference methods. Existing such methods require clusters to be asymptotically independent. Under mild conditions, we prove that, for this requirement to hold for network‐dependent data, it is necessary and sufficient that clusters have low conductance, the ratio of edge boundary size to volume. This yields a simple measure of cluster quality. We find in simulations that when clusters have low conductance, cluster‐robust methods control size better than HAC estimators. However, for important classes of networks lacking low‐conductance clusters, the former can exhibit substantial size distortion. To determine the number of low‐conductance clusters and construct them, we draw on results in spectral graph theory that connect conductance to the spectrum of the graph Laplacian. Based on these results, we propose to use the spectrum to determine the number of low‐conductance clusters and spectral clustering to construct them.
网络簇-鲁棒推理
由于网络数据通常由来自单个大型网络的观测数据组成,研究人员经常将网络划分为簇,以便应用聚类鲁棒推理方法。现有的这种方法要求聚类是渐近独立的。在温和的条件下,我们证明了对于网络相关数据的这一要求,集群具有低电导,边缘边界大小与体积的比率是必要和充分的。这产生了一个简单的集群质量度量。我们在模拟中发现,当簇具有低电导时,簇鲁棒方法比HAC估计器更好地控制大小。然而,对于缺乏低电导簇的重要网络类别,前者可能表现出严重的尺寸扭曲。为了确定低电导簇的数量并构造它们,我们借鉴了谱图理论中将电导与图拉普拉斯的谱联系起来的结果。基于这些结果,我们建议使用光谱来确定低电导簇的数量,并使用光谱聚类来构建它们。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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