{
  "id": "2102.08020",
  "version": "v1",
  "published": "2021-02-16T08:36:28.000Z",
  "updated": "2021-02-16T08:36:28.000Z",
  "title": "Concentration of measure and generalized product ofrandom vectors with an application to Hanson-Wright-like inequalities",
  "authors": [
    "Cosme Louart",
    "Romain Couillet"
  ],
  "comment": "48 pages",
  "categories": [
    "math.PR",
    "stat.ML"
  ],
  "abstract": "Starting from concentration of measure hypotheses on $m$ random vectors $Z_1,\\ldots, Z_m$, this article provides an expression of the concentration of functionals $\\phi(Z_1,\\ldots, Z_m)$ where the variations of $\\phi$ on each variable depend on the product of the norms (or semi-norms) of the other variables (as if $\\phi$ were a product). We illustrate the importance of this result through various generalizations of the Hanson-Wright concentration inequality as well as through a study of the random matrix $XDX^T$ and its resolvent $Q = (I_p - \\frac{1}{n}XDX^T)^{-1}$, where $X$ and $D$ are random, which have fundamental interest in statistical machine learning applications.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-16T08:36:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60-08",
      "60B20",
      "62J07",
      "G.3"
    ],
    "keywords": [
      "generalized product ofrandom vectors",
      "hanson-wright-like inequalities",
      "hanson-wright concentration inequality",
      "measure hypotheses",
      "random matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}