论文标题
基于光谱的网络人群中假设检验的框架
A spectral-based framework for hypothesis testing in populations of networks
论文作者
论文摘要
在本文中，我们提出了一种基于光谱的新方法，用于针对网络人群的假设检验。主要目标是开发测试，以确定两个给定的网络样本是否来自相同的随机模型或分布。我们的测试统计量基于中心和缩放的邻接矩阵的三阶轨迹，我们证明，随着节点的数量倾向于无穷大。还提供了测试的渐近功率保证。在表征提出的测试统计的理论属性时，探索了网络数量与每个网络的节点数量之间的适当相互作用。我们的测试适用于二进制和加权网络，在一个非常通用的框架下运行，该框架允许网络较大且稀疏，并且可以扩展到多样本测试。我们提供了一项广泛的仿真研究，以证明我们的测试优于现有方法，并将测试应用于三个真实数据集。
In this paper, we propose a new spectral-based approach to hypothesis testing for populations of networks. The primary goal is to develop a test to determine whether two given samples of networks come from the same random model or distribution. Our test statistic is based on the trace of the third order for a centered and scaled adjacency matrix, which we prove converges to the standard normal distribution as the number of nodes tends to infinity. The asymptotic power guarantee of the test is also provided. The proper interplay between the number of networks and the number of nodes for each network is explored in characterizing the theoretical properties of the proposed testing statistics. Our tests are applicable to both binary and weighted networks, operate under a very general framework where the networks are allowed to be large and sparse, and can be extended to multiple-sample testing. We provide an extensive simulation study to demonstrate the superior performance of our test over existing methods and apply our test to three real datasets.
