Collaborative non-parametric two-sample testing

This paper addresses the multiple two-sample test problem in a graph-structured setting, which is a common scenario in fields such as Spatial Statistics and Neuroscience. Each node v in fixed graph deals with a two-sample testing problem between two node-specific probability density functions (pdfs), pv and qv. The goal is to identify nodes where the null hypothesis pv = qv should be rejected, under the assumption that connected nodes would yield similar test outcomes. We propose the non-parametric collaborative two-sample testing (CTST) framework that efficiently leverages the graph structure and minimizes the assumptions over pv and qv. Our methodology integrates elements from f-divergence estimation, Kernel Methods, and Multitask Learning. We use synthetic experiments and a real sensor network detecting seismic activity to demonstrate that CTST outperforms state-of-the-art non-parametric statistical tests that apply at each node independently, hence disregard the geometry of the problem.