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.

本研究提出了一种在图结构环境下解决多个双样本检验问题的方法，通过非参数协同双样本检验框架（CTST），利用图结构并最小化对概率密度函数的假设，综合了f-差异度估计、核方法和多任务学习的元素。通过合成实验和监测地震活动的传感器网络，证明CTST优于现有的非参数统计检验方法，因为该方法能够考虑问题的几何特性。

协同的非参数双样本测试