{
  "abstract": "We consider semi-supervised classification from a partially classified sample arising from a two-component Weibull mixture. The feature is observed for all data, whereas some class labels are missing. The probability of a missing label is modelled as a function of classification uncertainty, giving a feature-dependent missing-at-random (MAR) mechanism that shares parameters with the Weibull-mixture classifier. The missing-label indicators can therefore provide information about the classifier in addition to the observed features and available class labels. Under a common Weibull shape, a Bayes' rule has at most one positive decision boundary, which is unique when the rule is nonconstant; under unequal shapes, it can have two. We characterise these decision regions, derive the Fisher information for the classifier after adjustment for nuisance parameters in the missingness model, and obtain a decision-boundary expansion of the expected error rate of the plug-in sample rule relative to the Bayes error. The expansion yields classification-specific asymptotic relative efficiency formulas for the one- and two-boundary cases and shows that a positive-definite increase in Fisher information is sufficient, but not necessary, for a smaller first-order expected error rate. Numerical studies and a semi-synthetic analysis based on hard-drive failure data illustrate potential reductions in expected error rate and improvements in decision-boundary estimation from modelling feature-dependent label missingness.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00774",
  "author_total": 3,
  "authors": [
    {
      "name": "Jinran Wu"
    },
    {
      "name": "You-Gan Wang"
    },
    {
      "name": "Geoffrey J. McLachlan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6skde4a1fxmdd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00774",
  "fulltext_url": null,
  "id": "6skde4a1fxmdd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00774",
  "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.ML"
    ],
    [
      "openalex",
      "1702|Bayesian Methods and Mixture Models"
    ]
  ],
  "openalex": "W7206195559",
  "pdf_url": "https://arxiv.org/pdf/2609.00774",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6skde4a1fxmdd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:10Z",
      "native_id": "2609.00774",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00774"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Semi-Supervised Classification with Informative Missing Labels in Weibull Mixture Models",
  "title_text": "Semi-Supervised Classification with Informative Missing Labels in Weibull Mixture Models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:10Z",
  "url": "https://research.draconitic.com/paper/6skde4a1fxmdd",
  "venue": "arXiv",
  "versions": []
}