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Two-sample hypothesis testing for random graphs arises naturally in neuroscience, social networks, and machine learning.
In this talk we consider the problem of two-sample testing for two populations of inhomogeneous random graphs defined on the same set of n vertices, where the size of each population is much smaller than n.
The random graphs in each population are samples from a latent distance graphs model wherein edge probability between two vertices is given by some link function of distance between latent positions, and that both the matrix of latent positions and link functions are unknown and can differ between the two populations.
We propose a valid and consistent test for the hypothesis that the two random graphs have the same generating latent positions, up to some unidentifiable similarity transformation. Our test statistic is based on first estimating edge probabilities matrices by truncating singular value decompositions of averaged adjacency matrices in each population and then computing Spearman rho-correlation between these estimates. Application on a dataset of neural connectome graphs showed that we can distinguish between scans from different age groups.
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