# Collaborative non-parametric two-sample testing

arXiv: https://arxiv.org/abs/2402.05715 · HTML: https://mlsanity.com/paper/2402.05715/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 28 references that are in the map.
- First posted on arXiv 8 Feb 2024.

## Builds on (most cited first, 5 of 5)

- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [Generative Models and Model Criticism via Optimized Maximum Mean Discrepancy](https://mlsanity.com/paper/1611.04488/) (2016)
- [High-dimensional, multiscale online changepoint detection](https://mlsanity.com/paper/2003.03668/) (2020)
- [Multiple testing with the structure adaptive Benjamini-Hochberg algorithm](https://mlsanity.com/paper/1606.07926/) (2016)
- [Online non-parametric likelihood-ratio estimation by Pearson-divergence functional minimization](https://mlsanity.com/paper/2311.01900/) (2023)

## Abstract (arXiv)

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.