WITHDRAWN Efficient Two-Sample Hypothesis Testing for Large Networks : a Nonparametric Approach

Oregon Convention Center 

This paper provides an analysis of random networks, particularly in the context of two-sample hypothesis testing within the Random Dot Product Graph (RDPG) framework. We differentiate between semiparametric and nonparametric testing setups, with a focus on the latter, known for its versatility and size-independence between the vertex sets of two networks. The nonparametric setup starts with an assumption that all the vertices have a set of exchangeable latent distances that determines the interactions between them. The key question investigated here is the comparison between the two sets of latent distances from the two networks. Working with a U-statistic based nonparametric test statistic that approximates maximum mean discrepancy, we address computational challenges through a network subsampling method. Subsampling is a divide-and-conquer based method that reduces computation by analyzing smaller networks and then combining them. Our objectives include designing a subsampling-based method for estimating latent positions and validating the accuracy of a bootstrap-based testing procedure.

Two-sample hypothesis testing

Subsampling

Nonparametric

Random Dot Product Graph 

Section on Statistical Computing