{
  "abstract": "Cross-validation is a resampling procedure that provides a point estimate of generalization error for any predictive model. Cross-validation is widely used for model selection and evaluation. Uncertainty in the cross-validation estimate is challenging to quantify, and estimation of its variance is known to require multiple runs of the entire resampling procedure. Nested cross-validation computes a prediction interval for the generalization error for a given model and training dataset by resampling the entire cross-validation procedure but incurs extraordinary computational cost. We provide an efficient method for computing the nested cross-validation prediction interval using only a single model fit for some penalized regression models including ridge regression, spline smoothing, and some functional regression models. We characterize when our proposed method should be expected to out-perform resampling-based nested cross-validation in various scaling regimes as well as in finite samples. Experiments for functional principle components regression demonstrate non-trivial cases in which our proposed method improves run times substantially.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04126",
  "author_total": 2,
  "authors": [
    {
      "name": "Shuyang Cao"
    },
    {
      "name": "Alex Stringer"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/54wdrmxa13552.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04126",
  "fulltext_url": null,
  "id": "54wdrmxa13552",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04126",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.CO"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7208838812",
  "pdf_url": "https://arxiv.org/pdf/2609.04126",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/54wdrmxa13552.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:07Z",
      "native_id": "2609.04126",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04126"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.CO",
      "subfield": "statistics"
    }
  ],
  "title": "Fast Computation of Nested Cross-Validation for Penalized Regression",
  "title_text": "Fast Computation of Nested Cross-Validation for Penalized Regression",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:07Z",
  "url": "https://research.draconitic.com/paper/54wdrmxa13552",
  "venue": "arXiv",
  "versions": []
}