{
  "abstract": "Split conformal prediction provides finite-sample marginal coverage under exchangeability, but this guarantee averages over the random calibration sample. We study instead the law of the calibration-conditional coverage induced by a realized conformal threshold. In the continuous i.i.d. setting this law is exactly $Beta(k,n+1-k)$, so the usual marginal guarantee corresponds to its mean. We take this beta law as a finite-sample reference object and quantify departures from it using Wasserstein distances on $[0,1]$. The framework yields direct bounds on marginal coverage gaps and on bad-calibration probabilities, and separates different sources of non-i.i.d. behavior according to how they deform the beta reference: test-side shift acts through a transport map on the coverage scale, while calibration dependence changes the order-statistic law itself. We instantiate the framework in scale-shift, clustered, and stationary mixing settings, where the induced deformations can be characterized explicitly or through Berry-Esseen approximations. Simulations on dependent processes confirm that the first-order approximation tracks the empirical Wasserstein distance even at moderate sample sizes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Proceedings of Machine Learning Research 329, 133-168 (2026)",
  "arxiv": "2605.19024",
  "author_total": 3,
  "authors": [
    {
      "name": "Thiago R. Ramos"
    },
    {
      "name": "Helton Graziadei"
    },
    {
      "name": "Luben M. C. Cabezas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8f3gfpxan4fge.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.19024",
  "fulltext_url": null,
  "id": "8f3gfpxan4fge",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.19024",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7161829526",
  "pdf_url": "https://arxiv.org/pdf/2605.19024",
  "pmcid": null,
  "pmid": null,
  "published": "2026-05-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8f3gfpxan4fge.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:41Z",
      "native_id": "2605.19024",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.19024"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Conformal Prediction via Transported Beta Laws",
  "title_text": "Conformal Prediction via Transported Beta Laws",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:41Z",
  "url": "https://research.draconitic.com/paper/8f3gfpxan4fge",
  "venue": "arXiv",
  "versions": []
}