{
  "abstract": "Suppose we are given an ordered sequence of independent data whose distribution changes $K$ times at unknown locations, for some unknown $K \\geq 0$. In this paper, we study the problem of performing distribution-free inference on $K$. First, we show an impossibility result: any distribution-free upper confidence bound on $K$ must be trivial and uninformative. Then, using conformal $p$-values, and under only the assumption that the data segments induced by the changepoints are exchangeable (within themselves) and mutually independent, we construct a finite-sample valid lower confidence bound on $K$, which we call the Conformal LOwer bound on Changepoint Count (CLOCC). We show that CLOCC is the only feasible way to provide a lower bound on $K$ under the stated assumptions, a property we refer to as its universality. We provide practical guidelines for choosing score functions that yield efficient and tight lower bounds. We evaluate CLOCC in several synthetic and real-data experiments, where it provides informative lower bounds on $K$, demonstrating its practical applicability.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08234",
  "author_total": 2,
  "authors": [
    {
      "name": "Rohan Hore"
    },
    {
      "name": "Aaditya Ramdas"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/81946m0tvtg59.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08234",
  "fulltext_url": null,
  "id": "81946m0tvtg59",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08234",
  "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",
      "stat.ME"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1804|Advanced Statistical Process Monitoring"
    ]
  ],
  "openalex": "W7212087374",
  "pdf_url": "https://arxiv.org/pdf/2609.08234",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/81946m0tvtg59.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:07Z",
      "native_id": "2609.08234",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08234"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Distribution-free inference on the number of changepoints",
  "title_text": "Distribution-free inference on the number of changepoints",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:07Z",
  "url": "https://research.draconitic.com/paper/81946m0tvtg59",
  "venue": "arXiv",
  "versions": []
}