B0676
Title: SIMPLE: Statistical Inference on Membership Profiles in Large Networks
Authors: Xiao Han - University of Science and Technology of China (China) [presenting]
Abstract: Network data is prevalent in many contemporary big data applications in which the common interest is to unveil important latent links between different pairs of nodes. Yet a simple fundamental question of how to precisely quantify the statistical uncertainty associated with the identification of latent links still remains largely unexplored. We propose the method of statistical inference on membership profiles in large networks (SIMPLE) in the setting of a degree-corrected mixed membership model, where the null hypothesis assumes that the pair of nodes share the same profile of community memberships. Under some mild regularity conditions, we establish the exact limiting distributions of the two forms of SIMPLE test statistics under the null hypothesis and contiguous alternative hypothesis. They are the chi-square distributions and the non-central chi-square distributions, respectively, with degrees of freedom depending on whether the degrees are corrected or not. We also address the important issue of estimating the unknown number of communities and establishing the asymptotic properties of the associated test statistics. The advantages and practical utility of our new procedures in terms of both size and power are demonstrated through several simulation examples and real network applications.
