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Title: Two-sample tests for unweighted random graphs generated from latent space models Authors:  Xixi Hu - Indiana University Bloomington (United States) [presenting]
Michael Trosset - Indiana University Bloomington (United States)
Abstract: The problem of comparing graphs arises in many disciplines, including neuroscience, biology, and the social sciences. Treating graph comparison as a problem in statistical inference requires assuming a probability model that generates random graphs, e.g., a stochastic blockmodel or a latent space model in which each vertex is associated with a latent position and the probability of an edge between two vertices is a function of their latent positions. For latent space models, various methods have been suggested for testing the null hypothesis that two models with matched vertices are identical up to isometry. Previous work has emphasized the case in which one graph is generated by each model; it is not clear how to extend these methods to the case in which multiple graphs are generated by each model. If the edge probabilities are a known function of the Euclidean distance between the latent positions, then one can estimate two sets of common latent positions by metric multidimensional scaling (MDS) and construct a test statistic by Procrustes analysis. If the edge probability function is unknown but monotone, then one can use nonmetric MDS to construct scale-invariant representations of the common latent positions and proceed analogously. We investigate this procedure through simulations and apply our approach to real brain data, comparing the structural brain networks of subjects with autism to those of healthy controls.