{
  "id": "1704.00820",
  "version": "v1",
  "published": "2017-04-03T21:46:30.000Z",
  "updated": "2017-04-03T21:46:30.000Z",
  "title": "Principal Inertia Components and Applications",
  "authors": [
    "Flavio P. Calmon",
    "Ali Makhdoumi",
    "Muriel Médard",
    "Mayank Varia",
    "Mark Christiansen",
    "Ken R. Duffy"
  ],
  "comment": "Overlaps with arXiv:1405.1472 and arXiv:1310.1512",
  "categories": [
    "cs.IT",
    "math.IT"
  ],
  "abstract": "We explore properties and applications of the Principal Inertia Components (PICs) between two discrete random variables $X$ and $Y$. The PICs lie in the intersection of information and estimation theory, and provide a fine-grained decomposition of the dependence between $X$ and $Y$. Moreover, the PICs describe which functions of $X$ can or cannot be reliably inferred (in terms of MMSE) given an observation of $Y$. We demonstrate that the PICs play an important role in information theory, and they can be used to characterize information-theoretic limits of certain estimation problems. In privacy settings, we prove that the PICs are related to fundamental limits of perfect privacy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-03T21:46:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "principal inertia components",
      "applications",
      "discrete random variables",
      "privacy settings",
      "fundamental limits"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}