  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.
