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Title: Spectral-based tests for hypothesis testing on populations of networks Authors:  Lizhen Lin - The University of Notre Dame (United States) [presenting]
Li Chen - Sichuan University (China)
Nathan Josephs - Boston University (United States)
Jie Zhou - Sichuan University (China)
Eric Kolaczyk - Boston University (United States)
Abstract: The increasing prevalence of multiple network data in modern science and engineering calls for developments of models and theories that can deal with inference problems for populations of networks. We focus on addressing the problem of hypothesis testing for populations of networks and in particular, for differentiating distributions of two samples of networks. We consider a very general framework which allows us to perform tests on populations of large and sparse networks. We propose two spectral-based tests. The first test is based on the singular value of a generalized Wigner matrix. The asymptotic null distribution of the statistics is shown to follow the Tracy-Widom distribution as the number of nodes tends to infinity. The test also yields asymptotic power guarantee with the power tending to one under the alternative. The second spectral-based test statistic is based on the trace of the third-order for a centered and scaled adjacency matrix, which is proved to converge to the standard normal distribution N (0, 1) as nodes number tends to infinity. The proper interplay between the number of networks and the number of nodes for each network are explored. We also prove the asymptotic power guarantee for this test. Extensive simulation studies and real data analyses demonstrate the superior performance of our procedure with competitors.