{
  "abstract": "K-fold cross-validation (CV) is widely used as evidence of out-of-sample performance, although folds are neither independent experiments nor equally informative under heterogeneous data. Cross Upper-Bound Validation (CUBV) replaces point-wise CV accuracy by conservative upper bounds on true risk. Here we generalise CUBV through a single exponential framework in which the moment-generating function of the generalisation gap is controlled by a cumulant envelope gamma(lambda). This yields a family of risk bounds covering Hoeffding-, Bernstein-, dependency-aware, PAC-Bayesian, and heterogeneous source-fusion settings. For K-fold CV, dependence between fold-wise gaps is modelled through a joint sub-Gaussian proxy matrix. Under equicorrelation, this gives an effective number of folds, Keff = K/[1+(K-1)rho], showing that increasing K does not necessarily increase statistical evidence when folds are strongly dependent. The framework is also extended to posterior distributions over predictors and weighted multi-source fusion, where weights are selected by minimising an upper bound on future risk rather than empirical error alone. Experiments with trained linear classifiers on heterogeneous multimodal Gaussian mixtures compare K-fold CV with full-sample resubstitution plus risk correction. Bounds are evaluated by coverage and tightness. In low-dimensional small-sample settings, K-fold partitioning can increase uncertainty because individual folds under-represent minority modes, while corrected resubstitution can remain valid and tighter; this effect disappears as sample size increases. Overall, gamma-CUBV separates observed performance, uncertainty, dependence, model complexity, and confidence into explicit terms, providing a unified route from CV scores to risk statements and a principled validation criterion for heterogeneous small-sample applications such as neuroimaging.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.03465",
  "author_total": 1,
  "authors": [
    {
      "name": "JM Gorriz"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f60q0xexp458e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.03465",
  "fulltext_url": null,
  "id": "f60q0xexp458e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.03465",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "physics.data-an"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Machine Learning and Data Classification"
    ]
  ],
  "openalex": "W7220387687",
  "pdf_url": "https://arxiv.org/pdf/2610.03465",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f60q0xexp458e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:45Z",
      "native_id": "2610.03465",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.03465"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    },
    {
      "field": "physics",
      "origin": "arxiv:physics.data-an",
      "subfield": "computational"
    }
  ],
  "title": "When Is Accuracy Evidence? A Unified Theory of Generalisation, Validation, and Information Fusion",
  "title_text": "When Is Accuracy Evidence? A Unified Theory of Generalisation, Validation, and Information Fusion",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:56Z",
  "url": "https://research.draconitic.com/paper/f60q0xexp458e",
  "venue": "arXiv",
  "versions": []
}