A1670
Title: Network two-sample test for block models
Authors: Oscar Hernan Madrid Padilla - UCLA (United States) [presenting]
Abstract: The two-sample testing problem is considered for networks, where the goal is to determine whether two sets of networks originated from the same stochastic model. Assuming no vertex correspondence and allowing for different numbers of nodes, a fundamental network testing problem that goes beyond simple adjacency matrix comparisons is addressed. The stochastic block model (SBM) is adopted for network distributions due to their interpretability and the potential to approximate more general models. The lack of meaningful node labels and vertex correspondence translates to a graph-matching challenge when developing a test for SBMs. An efficient algorithm is introduced to match estimated network parameters, allowing the proper combination and contrast of information within and across samples, leading to a powerful test. It is shown that the matching algorithm and the overall test are consistent under mild conditions on the sparsity of the networks and the sample sizes, and a chi-squared asymptotic null distribution is derived for the test. Through a mixture of theoretical insights and empirical validations, including experiments with both synthetic and real-world data, robust statistical inference for complex network data is advanced.
