{
  "id": "2306.03955",
  "version": "v1",
  "published": "2023-06-06T18:33:40.000Z",
  "updated": "2023-06-06T18:33:40.000Z",
  "title": "Kernel Quadrature with Randomly Pivoted Cholesky",
  "authors": [
    "Ethan N. Epperly",
    "Elvira Moreno"
  ],
  "comment": "17 pages, 2 figures",
  "categories": [
    "math.NA",
    "cs.NA",
    "stat.ML"
  ],
  "abstract": "This paper presents new quadrature rules for functions in a reproducing kernel Hilbert space using nodes drawn by a sampling algorithm known as randomly pivoted Cholesky. The resulting computational procedure compares favorably to previous kernel quadrature methods, which either achieve low accuracy or require solving a computationally challenging sampling problem. Theoretical and numerical results show that randomly pivoted Cholesky is fast and achieves comparable quadrature error rates to more computationally expensive quadrature schemes based on continuous volume sampling, thinning, and recombination. Randomly pivoted Cholesky is easily adapted to complicated geometries with arbitrary kernels, unlocking new potential for kernel quadrature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-06-06T18:33:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "randomly pivoted cholesky",
      "achieves comparable quadrature error rates",
      "kernel quadrature methods",
      "reproducing kernel hilbert space",
      "achieve low accuracy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}