{
  "abstract": "In multivariate conformal prediction, many nonconformity scores yield prediction sets with complex geometry (e.g., ellipsoids or density level sets) that are difficult to interpret and visualize. Hyperrectangles offer a practical alternative by providing one interval per output. We extend this notion to Cartesian products of arbitrary one-dimensional sets, which we call generalized hyperrectangles. We introduce a rectangularization framework that turns any continuous multivariate nonconformity score, or conditional density, into one yielding generalized hyperrectangular prediction sets with finite-sample coverage. We establish key geometric properties of our rectangularization framework and provide useful intuitions on generalized hyperrectangles. We further establish a representation theorem showing that a broad class of hyperrectangular conformal methods based on max-aggregated coordinate-wise scores can be interpreted as rectangularizations of implicit conditional densities. Through synthetic and real-world experiments, we quantify the efficiency cost of rectangularization, while highlighting its benefits, especially for practical applications of uncertainty quantification.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.05543",
  "author_total": 2,
  "authors": [
    {
      "name": "Nabil Alami"
    },
    {
      "name": "Souhaib Ben Taieb"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ewsjgm18bm19b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.05543",
  "fulltext_url": null,
  "id": "ewsjgm18bm19b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.05543",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "stat.ML"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.05543",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ewsjgm18bm19b.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:06Z",
      "native_id": "2611.05543",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.05543"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Generalized Hyperrectangular Prediction Sets in Multivariate Conformal Prediction",
  "title_text": "Generalized Hyperrectangular Prediction Sets in Multivariate Conformal Prediction",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:32Z",
  "url": "https://research.draconitic.com/paper/ewsjgm18bm19b",
  "venue": "arXiv",
  "versions": []
}