{
  "id": "2207.06503",
  "version": "v1",
  "published": "2022-07-13T19:51:24.000Z",
  "updated": "2022-07-13T19:51:24.000Z",
  "title": "Randomly pivoted Cholesky: Practical approximation of a kernel matrix with few entry evaluations",
  "authors": [
    "Yifan Chen",
    "Ethan N. Epperly",
    "Joel A. Tropp",
    "Robert J. Webber"
  ],
  "comment": "28 pages, 4 figures",
  "categories": [
    "math.NA",
    "cs.NA",
    "stat.ML"
  ],
  "abstract": "Randomly pivoted Cholesky (RPCholesky) is a natural algorithm for computing a rank-k approximation of an N x N positive semidefinite (psd) matrix. RPCholesky can be implemented with just a few lines of code. It requires only (k+1)N entry evaluations and O(k^2 N) additional arithmetic operations. This paper offers the first serious investigation of its experimental and theoretical behavior. Empirically, RPCholesky matches or improves on the performance of alternative algorithms for low-rank psd approximation. Furthermore, RPCholesky provably achieves near-optimal approximation guarantees. The simplicity, effectiveness, and robustness of this algorithm strongly support its use in scientific computing and machine learning applications.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-13T19:51:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "65F55",
      "65C99",
      "68T05"
    ],
    "keywords": [
      "randomly pivoted cholesky",
      "entry evaluations",
      "kernel matrix",
      "practical approximation",
      "provably achieves near-optimal approximation guarantees"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}