{
  "id": "2107.01975",
  "version": "v1",
  "published": "2021-07-05T12:30:02.000Z",
  "updated": "2021-07-05T12:30:02.000Z",
  "title": "The information loss of a stochastic map",
  "authors": [
    "James Fullwood",
    "Arthur J. Parzygnat"
  ],
  "comment": "31 pages",
  "categories": [
    "cs.IT",
    "math.CT",
    "math.IT",
    "math.PR"
  ],
  "abstract": "We provide a stochastic extension of the Baez-Fritz-Leinster characterization of the Shannon information loss associated with a measure-preserving function. This recovers the conditional entropy and a closely related information-theoretic measure that we call `conditional information loss.' Although not functorial, these information measures are semi-functorial, a concept we introduce that is definable in any Markov category. We also introduce the notion of an `entropic Bayes' rule' for information measures, and we provide a characterization of conditional entropy in terms of this rule.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-05T12:30:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "94A17",
      "18A05",
      "62F15"
    ],
    "keywords": [
      "stochastic map",
      "information measures",
      "conditional entropy",
      "conditional information loss",
      "shannon information loss"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}