{
  "abstract": "By slightly adapting Wang's recent important argument for the homoscedastic setting, we prove that every finite heteroscedastic Gaussian mixture has only finitely many critical points, and, consequently, only finitely many modes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30334",
  "author_total": 1,
  "authors": [
    {
      "name": "Akifumi Okuno"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0v3wtp11v8d3d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30334",
  "fulltext_url": null,
  "id": "0v3wtp11v8d3d",
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  "landing_url": "https://arxiv.org/abs/2608.30334",
  "language": null,
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  "licence_label": "arXiv licence",
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "math.ST"
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    [
      "arxiv",
      "stat.TH"
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      "openalex",
      "1702|Bayesian Methods and Mixture Models"
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  "openalex": "W7204937806",
  "pdf_url": "https://arxiv.org/pdf/2608.30334",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0v3wtp11v8d3d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30334",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30334"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Unconditional Finiteness of the Number of Critical Points of Gaussian Mixture Densities",
  "title_text": "Unconditional Finiteness of the Number of Critical Points of Gaussian Mixture Densities",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:54Z",
  "url": "https://research.draconitic.com/paper/0v3wtp11v8d3d",
  "venue": "arXiv",
  "versions": []
}