{
  "id": "2104.05360",
  "version": "v1",
  "published": "2021-04-12T11:25:56.000Z",
  "updated": "2021-04-12T11:25:56.000Z",
  "title": "Statistical inference of finite-rank tensors",
  "authors": [
    "Hong-Bin Chen",
    "Jean-Christophe Mourrat",
    "Jiaming Xia"
  ],
  "comment": "21 pages",
  "categories": [
    "math.PR",
    "cond-mat.dis-nn",
    "cs.IT",
    "math.IT"
  ],
  "abstract": "We consider a general statistical inference model of finite-rank tensor products. For any interaction structure and any order of tensor products, we identify the limit free energy of the model in terms of a variational formula. Our approach consists of showing first that the limit free energy must be the viscosity solution to a certain Hamilton-Jacobi equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-12T11:25:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B44",
      "82D30"
    ],
    "keywords": [
      "limit free energy",
      "general statistical inference model",
      "finite-rank tensor products",
      "interaction structure",
      "variational formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}