{
  "abstract": "When providing forecasted probabilities with a predictive model, the ideal model offers perfect calibration: the true probability of the outcome (i.e., the probability that $Y=1$) exactly matches the forecasted probability $f(X)$. In practice, models inevitably exhibit calibration error, and it is therefore important to be able to measure this miscalibration to assess a model's reliability. The Expected Calibration Error (ECE) is the most widely used measure of miscalibration, but is known to be impossible to estimate the ECE with guaranteed accuracy in an assumption-free setting. In this work, we propose an alternative measure, the rankECE, that is based on comparing points with neighboring values of the predicted probability $f(X)$. Our theoretical guarantees and empirical results establish that rankECE provides a better proxy for ECE as compared to binned approximations to ECE, which are the most commonly-used approximations in practice.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13100",
  "author_total": 2,
  "authors": [
    {
      "name": "Anirban Chatterjee"
    },
    {
      "name": "Rina Foygel Barber"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/asr8a9t6kgsbc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13100",
  "fulltext_url": null,
  "id": "asr8a9t6kgsbc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13100",
  "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",
      "1702|Machine Learning and Data Classification"
    ]
  ],
  "openalex": "W7213121425",
  "pdf_url": "https://arxiv.org/pdf/2609.13100",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/asr8a9t6kgsbc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:17Z",
      "native_id": "2609.13100",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13100"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "A Ranking Approach for Measuring Calibration",
  "title_text": "A Ranking Approach for Measuring Calibration",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:17Z",
  "url": "https://research.draconitic.com/paper/asr8a9t6kgsbc",
  "venue": "arXiv",
  "versions": []
}