Networks arise naturally in many scientific fields as a representation of pairwise connections. Statistical network analysis has most often considered a single large network, but it is common in a number of applications to observe multiple networks on a shared node set. When these networks are grouped by case-control status or another categorical covariate, the classical statistical question of two-sample comparison arises. In this work, we address the problem of testing for statistically significant differences in a given arbitrary subset of connections. This general framework allows an analyst to focus on a single node, a specific region of interest, or compare whole networks. Our ability to conduct ``mesoscale'' testing on a meaningful group of edges is particularly relevant for applications such as neuroimaging and distinguishes our approach from prior work, which tends to focus either on a single node or the whole network. In this mesoscale setting, we develop statistically sound projection-based tests for two-sample comparison in both weighted and binary edge networks. The key to our approach is to leverage network information from outside the set of interest to learn informative low-rank projections which leads to more powerful tests.

翻译：网络作为成对连接的表示，在许多科学领域中自然出现。统计网络分析通常考虑单个大型网络，但在许多应用中，观察共享节点集上的多个网络是常见的。当这些网络按病例-对照状态或其他分类协变量分组时，经典的统计双样本比较问题便随之产生。在这项工作中，我们解决了在给定任意连接子集中检验统计显著差异的问题。这一通用框架允许分析人员专注于单个节点、特定感兴趣区域或比较整个网络。我们能够对一组有意义的边进行"中尺度"检验，这对于神经影像学等应用尤其相关，并将我们的方法与先前主要关注单个节点或整个网络的研究区分开来。在此中尺度设置下，我们为加权和二元边网络中的双样本比较开发了基于统计可靠投影的检验方法。我们方法的关键在于利用感兴趣集合之外的网络信息来学习信息丰富的低秩投影，从而实现更有效的检验。