A1216
Title: Testing large random graphs of unequal size with applications to fMRI data
Authors: Xin Jin - The University of Tampa (United States) [presenting]
Kit Chan - Bowling Green State University (United States)
Ian Barnett - University of Pennsylvania (United States)
Riddhi Pratim Ghosh - Bowling Green State University (United States)
Abstract: Two-sample hypothesis testing for large graphs is increasingly important in cognitive science, probabilistic machine learning, and artificial intelligence. While numerous methods have been proposed, less attention has been given to settings involving unequal graph sizes or only one or a few graph samples. An efficient sequential two-stage procedure is proposed for such scenarios. In the first stage, spectral clustering is applied to each graph to estimate the number of communities and screen for structural compatibility. In the second stage, bootstrapped adjacency matrices are generated from estimated community-wise edge probability matrices to construct a Frobenius test statistic. The asymptotic distribution of the statistic is established, and extensive simulations show that the procedure is stable, efficient, and effective in detecting subtle structural differences while providing rigorous theoretical guarantees. Its utility is illustrated on fMRI data, where brain activity patterns under sentence, picture, and control stimuli are successfully distinguished.
