Two-Sample Tests for Graphs with Applications in Neuroscience

• Activity Number: 471 - Advances in High-Dimensional Inference and Multiple Testing
• Type: Contributed
• Date/Time: Wednesday, July 31, 2019 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Xixi Hu* and Michael Trosset and Minh Tang
• Companies: Indiana University Bloomington and Indiana University Bloomington and Johns Hopkins University
• Keywords: two-sample test; latent space model; multidimensional scaling; brain networks

Abstract

Two-sample graph comparison arises in neuroscience, e.g., when comparing the brain networks of people from two populations. Standard practices include tests on aggregated univariate measures, which may not fully characterize a graph, or one test for each edge, which does not exploit graph structure. Assuming a latent space model (LSM) for random graphs, we propose an inferential framework that both compares entire graphs and utilizes underlying structure. Graphs in LSM are described by a set of latent positions and a function that maps distance to edge probability. Our method estimates two sets of common latent positions by multidimensional scaling, then constructs a test statistic by comparing interpoint distance matrices. Simulations show that our test has greater power than either the standard practices or a direct comparison of sample mean graphs. We apply our approach to compare the structural brain networks of (a) autistic vs healthy subjects, and (b) young vs old adults.