{
  "id": "2105.11425",
  "version": "v1",
  "published": "2021-05-24T17:33:19.000Z",
  "updated": "2021-05-24T17:33:19.000Z",
  "title": "Uncertainty quantification for distributed regression",
  "authors": [
    "Valeriy Avanesov"
  ],
  "categories": [
    "stat.ML",
    "cs.LG"
  ],
  "abstract": "The ever-growing size of the datasets renders well-studied learning techniques, such as Kernel Ridge Regression, inapplicable, posing a serious computational challenge. Divide-and-conquer is a common remedy, suggesting to split the dataset into disjoint partitions, obtain the local estimates and average them, it allows to scale-up an otherwise ineffective base approach. In the current study we suggest a fully data-driven approach to quantify uncertainty of the averaged estimator. Namely, we construct simultaneous element-wise confidence bands for the predictions yielded by the averaged estimator on a given deterministic prediction set. The novel approach features rigorous theoretical guaranties for a wide class of base learners with Kernel Ridge regression being a special case. As a by-product of our analysis we also obtain a sup-norm consistency result for the divide-and-conquer Kernel Ridge Regression. The simulation study supports the theoretical findings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-24T17:33:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "uncertainty quantification",
      "distributed regression",
      "simultaneous element-wise confidence bands",
      "features rigorous theoretical guaranties",
      "renders well-studied learning techniques"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}