{
  "id": "2107.14184",
  "version": "v1",
  "published": "2021-07-29T17:11:13.000Z",
  "updated": "2021-07-29T17:11:13.000Z",
  "title": "Wasserstein Conditional Independence Testing",
  "authors": [
    "Andrew Warren"
  ],
  "comment": "32 pages",
  "categories": [
    "math.ST",
    "math.OC",
    "stat.TH"
  ],
  "abstract": "We introduce a test for the conditional independence of random variables $X$ and $Y$ given a random variable $Z$, specifically by sampling from the joint distribution $(X,Y,Z)$, binning the support of the distribution of $Z$, and conducting multiple $p$-Wasserstein two-sample tests. Under a $p$-Wasserstein Lipschitz assumption on the conditional distributions $\\mathcal{L}_{X|Z}$, $\\mathcal{L}_{Y|Z}$, and $\\mathcal{L}_{(X,Y)|Z}$, we show that it is possible to control the Type I and Type II error of this test, and give examples of explicit finite-sample error bounds in the case where the distribution of $Z$ has compact support.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-29T17:11:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "62G10",
      "49Q22"
    ],
    "keywords": [
      "wasserstein conditional independence testing",
      "explicit finite-sample error bounds",
      "wasserstein two-sample tests",
      "wasserstein lipschitz assumption",
      "random variable"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}