{
  "abstract": "Unsupervised clustering is widely used to discover underlying group structure, after which researchers often seek to validate these groups via post-hoc hypothesis testing on the population means. However, using the same data both to form clusters and to test for a difference in means inflates the Type I error rate. Recent work in selective inference has proposed solutions when the underlying data are drawn from a multivariate Gaussian distribution with a known covariance matrix or an unknown isotropic covariance matrix. We propose a new selective test for the difference in means between two clusters that provably controls the Type I error rate under an arbitrary unknown covariance matrix. Our test statistic does not require estimating the feature covariance matrix; instead, it leverages a Monte Carlo sampling procedure over the set of orthogonal matrices. We show that this new selective test can be computed efficiently, and we derive closed-form solutions when clusters are formed using k-means or hierarchical clustering. In simulations, we demonstrate that our proposed p-value controls the selective Type I error rate and achieves substantial power, and we illustrate its application on gene expression and drug review data sets.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17458",
  "author_total": 2,
  "authors": [
    {
      "name": "Yiqun T. Chen"
    },
    {
      "name": "Lucy L. Gao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3jtgnxxjkma8d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17458",
  "fulltext_url": null,
  "id": "3jtgnxxjkma8d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17458",
  "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.AP"
    ],
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7221767018",
  "pdf_url": "https://arxiv.org/pdf/2610.17458",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3jtgnxxjkma8d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:26Z",
      "native_id": "2610.17458",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17458"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.AP",
      "subfield": "statistics"
    }
  ],
  "title": "Selective Inference for Clustering Under Unknown Covariance",
  "title_text": "Selective Inference for Clustering Under Unknown Covariance",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:26Z",
  "url": "https://research.draconitic.com/paper/3jtgnxxjkma8d",
  "venue": "arXiv",
  "versions": []
}