{
  "id": "1808.09933",
  "version": "v1",
  "published": "2018-08-29T17:21:17.000Z",
  "updated": "2018-08-29T17:21:17.000Z",
  "title": "Certified Mapper: Repeated testing for acyclicity and obstructions to the nerve lemma",
  "authors": [
    "Mikael Vejdemo-Johansson",
    "Alisa Leshchenko"
  ],
  "comment": "16 pages, submitted to the proceedings of the Abel symposium",
  "categories": [
    "math.AT",
    "cs.LG",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "The Mapper algorithm does not include a check for whether the cover produced conforms to the requirements of the nerve lemma. To perform a check for obstructions to the nerve lemma, statistical considerations of multiple testing quickly arise. In this paper, we propose several statistical approaches to finding obstructions: through a persistent nerve lemma, through simulation testing, and using a parametric refinement of simulation tests. We suggest Certified Mapper -- a method built from these approaches to generate certificates of non-obstruction, or identify specific obstructions to the nerve lemma -- and we give recommendations for which statistical approaches are most appropriate for the task.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-29T17:21:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "certified mapper",
      "repeated testing",
      "acyclicity",
      "statistical approaches",
      "persistent nerve lemma"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}