{
  "abstract": "We introduce a conformal prediction framework for regression with Grassmann-valued responses. The proposed method constructs prediction regions in the form of metric balls directly on the Grassmann manifold, using basis-invariant geometric distances as non-conformity measures and scaling the corresponding non-conformity scores through a learned prediction difficulty estimator. This yields locally adaptive, input-dependent prediction regions that respect the underlying manifold geometry, while retaining the finite-sample marginal coverage guarantee of split conformal prediction under exchangeability. We evaluate several Grassmannian distance metrics and compare their prediction-region efficiency on synthetic benchmarks and an airfoil inverse shape-design problem. The results highlight the advantages of geometry-aware non-conformity scores, while local adaptation improves empirical coverage uniformity across prediction difficulty levels and, in strongly heteroscedastic settings, can substantially reduce prediction-region size while maintaining the target coverage.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.23508",
  "author_total": 3,
  "authors": [
    {
      "name": "Dimitrios Loukrezis"
    },
    {
      "name": "Zachary J. Grey"
    },
    {
      "name": "Dimitris G. Giovanis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/50gs7t295tsrr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.23508",
  "fulltext_url": null,
  "id": "50gs7t295tsrr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.23508",
  "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",
      "2613|Advanced Statistical Methods and Models"
    ]
  ],
  "openalex": "W7222935523",
  "pdf_url": "https://arxiv.org/pdf/2610.23508",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/50gs7t295tsrr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:43Z",
      "native_id": "2610.23508",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.23508"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Adaptive conformal prediction on the Grassmannian",
  "title_text": "Adaptive conformal prediction on the Grassmannian",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:38Z",
  "url": "https://research.draconitic.com/paper/50gs7t295tsrr",
  "venue": "arXiv",
  "versions": []
}