{
  "abstract": "The double-descent phenomenon observed in modern machine learning models has challenged the classical bias-variance trade-off by showing that prediction error can decrease again as model complexity exceeds the interpolation threshold. Although this phenomenon has been extensively studied for deep neural networks and other high-capacity models, its implications for classical statistical methods remain less well understood. In this paper, we investigate double descent in linear discriminant analysis (LDA), a fundamental classification method for binary classification. Using random matrix theory, we derive the asymptotic misclassification risk of LDA in the high-dimensional regime where the dimension (p) and sample size (n) satisfy (p/n \\to γ). Specifically, we obtain an explicit asymptotic expression for the LDA risk with a general population covariance matrix when (γ\\in (0,1)), and for the Moore-Penrose pseudo-inverse LDA classifier under an isotropic covariance model when (γ\\in (1,\\infty)). Together, these results provide a complete characterization of the double-descent risk curve of LDA across both the under- and over-parameterized regimes. Simulation studies and experiments on the ARCENE cancer classification dataset demonstrate close agreement with the theoretical predictions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.19061",
  "author_total": 4,
  "authors": [
    {
      "name": "Yonghe Lu"
    },
    {
      "name": "Han Lin Shang"
    },
    {
      "name": "Yanrong Yang"
    },
    {
      "name": "Kehan Zhao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/050kv82kaj3yz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.19061",
  "fulltext_url": null,
  "id": "050kv82kaj3yz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.19061",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.ME"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.19061",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/050kv82kaj3yz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:10Z",
      "native_id": "2609.19061",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.19061"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Double Descent in High-dimensional Linear Discriminant Analysis",
  "title_text": "Double Descent in High-dimensional Linear Discriminant Analysis",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:10Z",
  "url": "https://research.draconitic.com/paper/050kv82kaj3yz",
  "venue": "arXiv",
  "versions": []
}