{
  "id": "2010.07064",
  "version": "v1",
  "published": "2020-10-14T13:09:48.000Z",
  "updated": "2020-10-14T13:09:48.000Z",
  "title": "Optimal Quantisation of Probability Measures Using Maximum Mean Discrepancy",
  "authors": [
    "Onur Teymur",
    "Jackson Gorham",
    "Marina Riabiz",
    "Chris. J. Oates"
  ],
  "categories": [
    "stat.ML",
    "cs.LG",
    "stat.CO",
    "stat.ME"
  ],
  "abstract": "Several researchers have proposed minimisation of maximum mean discrepancy (MMD) as a method to quantise probability measures, i.e., to approximate a target distribution by a representative point set. Here we consider sequential algorithms that greedily minimise MMD over a discrete candidate set. We propose a novel non-myopic algorithm and, in order to both improve statistical efficiency and reduce computational cost, we investigate a variant that applies this technique to a mini-batch of the candidate set at each iteration. When the candidate points are sampled from the target, the consistency of these new algorithm - and their mini-batch variants - is established. We demonstrate the algorithms on a range of important computational problems, including optimisation of nodes in Bayesian cubature and the thinning of Markov chain output.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-14T13:09:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "maximum mean discrepancy",
      "optimal quantisation",
      "discrete candidate set",
      "reduce computational cost",
      "quantise probability measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}