Improving the Power of a Two-Sample Graph Test with Applications in Connectomics.

In many applications, there is interest in testing whether two graphs come from the same distribution. However, due to the nature of graph data, classical statistical methods are not directly applicable. When the distribution of each graph is determined by a distribution for vertex latent positions, in particular under the random dot product graph model, a statistical procedure is derived to test whether the two sets of latent positions are equally distributed. We empirically analyze several methods for this problem, and show that adapting Optimal Transport Procrustes (OPT) for aligning latent positions and multiscale graph correlation (MGC) for hypothesis testing to answer this question results in a test which outperforms several existing methods.