{
  "id": "1904.05294",
  "version": "v1",
  "published": "2019-04-10T16:57:41.000Z",
  "updated": "2019-04-10T16:57:41.000Z",
  "title": "Hamilton-Jacobi equations for finite-rank matrix inference",
  "authors": [
    "Jean-Christophe Mourrat"
  ],
  "comment": "26 pages",
  "categories": [
    "math.PR",
    "cond-mat.dis-nn"
  ],
  "abstract": "We compute the large-scale limit of the free energy associated with the problem of inference of a finite-rank matrix. The method follows the principle put forward in arXiv:1811.01432 which consists in identifying a suitable Hamilton-Jacobi equation satisfied by the limit free energy. We simplify the approach of arXiv:1811.01432 using a notion of weak solution of the Hamilton-Jacobi equation which is more convenient to work with and is applicable whenever the non-linearity in the equation is convex.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-10T16:57:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B44",
      "82D30"
    ],
    "keywords": [
      "finite-rank matrix inference",
      "limit free energy",
      "suitable hamilton-jacobi equation",
      "large-scale limit",
      "weak solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}