Collaborative non-parametric two-sample testing
This work addresses the challenge of efficiently identifying distribution differences in interconnected data for fields like spatial statistics and neuroscience, representing an incremental improvement by integrating existing methods to exploit graph structure.
The paper tackles the problem of multiple two-sample testing in graph-structured settings, such as spatial statistics and neuroscience, by proposing a non-parametric collaborative framework (CTST) that leverages graph connections to improve detection of nodes where probability distributions differ, outperforming independent node tests in synthetic and real-world seismic activity detection.
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), $p_v$ and $q_v$. The goal is to identify nodes where the null hypothesis $p_v = q_v$ 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 $p_v$ and $q_v$. 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.