{
  "id": "2009.08735",
  "version": "v1",
  "published": "2020-09-18T10:27:04.000Z",
  "updated": "2020-09-18T10:27:04.000Z",
  "title": "Convergence of unadjusted Hamiltonian Monte Carlo for mean-field models",
  "authors": [
    "Nawaf Bou-Rabee",
    "Katharina Schuh"
  ],
  "comment": "35 pages, 6 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We present dimension-free convergence and discretization error bounds for the unadjusted Hamiltonian Monte Carlo algorithm applied to high-dimensional probability distributions of mean-field type. These bounds require the discretization step to be sufficiently small, but do not require strong convexity of either the unary or pairwise potential terms present in the mean-field model. To handle high dimensionality, our proof uses a particlewise coupling that is contractive in a complementary particlewise metric.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-18T10:27:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J05",
      "65P10",
      "65C05"
    ],
    "keywords": [
      "mean-field model",
      "convergence",
      "unadjusted hamiltonian monte carlo algorithm",
      "discretization error bounds",
      "high-dimensional probability distributions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}