Collaborative non-parametric two-sample testing
<|reference_start|>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), $p_v$ 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.<|reference_end|>
@article{de la concha2024collaborative,
    title={Collaborative non-parametric two-sample testing},
    author={Alejandro de la Concha, Nicolas Vayatis, Argyris Kalogeratos},
    journal={arXiv preprint arXiv:2402.05715},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.05715},
    primaryClass={stat.ML cs.LG}
}