{
  "id": "2202.03951",
  "version": "v1",
  "published": "2022-02-08T16:01:38.000Z",
  "updated": "2022-02-08T16:01:38.000Z",
  "title": "On Sibson's $α$-Mutual Information",
  "authors": [
    "Amedeo Roberto Esposito",
    "Adrien Vandenbroucque",
    "Michael Gastpar"
  ],
  "comment": "Submitted to ISIT 2022",
  "categories": [
    "cs.IT",
    "math.IT",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "We explore a family of information measures that stems from R\\'enyi's $\\alpha$-Divergences with $\\alpha<0$. In particular, we extend the definition of Sibson's $\\alpha$-Mutual Information to negative values of $\\alpha$ and show several properties of these objects. Moreover, we highlight how this family of information measures is related to functional inequalities that can be employed in a variety of fields, including lower-bounds on the Risk in Bayesian Estimation Procedures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-08T16:01:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mutual information",
      "information measures",
      "bayesian estimation procedures",
      "functional inequalities",
      "definition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}