{
  "id": "2402.05715",
  "version": "v1",
  "published": "2024-02-08T14:43:56.000Z",
  "updated": "2024-02-08T14:43:56.000Z",
  "title": "Collaborative non-parametric two-sample testing",
  "authors": [
    "Alejandro de la Concha",
    "Nicolas Vayatis",
    "Argyris Kalogeratos"
  ],
  "categories": [
    "stat.ML",
    "cs.LG"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-02-08T14:43:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "collaborative non-parametric two-sample testing",
      "state-of-the-art non-parametric statistical tests",
      "network detecting seismic activity",
      "outperforms state-of-the-art non-parametric statistical",
      "ctst outperforms state-of-the-art non-parametric"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}