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Friday, October 19
Fri, Oct 19, 5:15 PM - 6:30 PM
Hall of Mirrors
Celebrating Women in Statistics and Data Science Reception and Speed Poster 3, Sponsored by Google and 84.51°

Two-Sample Tests for Unweighted Random Graphs Generated from Latent Space Models (304973)

*Xixi Hu, Indiana University Bloomington 
Michael Trosset, Indiana University Bloomington 

Keywords: latent space model, graph inference, two-sample hypothesis testing

Treating graph comparison as a problem in statistical inference requires a probability model that generates random graphs, e.g., a stochastic blockmodel or a latent space model (LSM) in which vertices are associated with latent positions and the probability of an edge between two vertices is a function of their latent positions. Various methods have been suggested for testing the null hypothesis that two LSMs with matched vertices are identical up to isometry, but it is unclear how to extend these methods from the case of one graph generated by each LSM to the case of multiple graphs. 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 study this procedure through simulation and use it to compare the structural brain networks of subjects with autism to those of controls.