{
  "abstract": "This paper establishes high-probability, non-asymptotic upper bounds for the population excess risk of minimum $\\ell_q$-norm interpolating estimators in linear regression, valid for all $1<q<\\infty$ under three scenarios: convex concentration, mild moment assumptions and log-concavity. Consequently, we derive sufficient conditions for these estimators to exhibit benign overfitting. Our analysis hinges on a Feature Space Decomposition (FSD) framework, which naturally highlights the self-regularizing properties of minimum norm interpolants as well as the role of alignment between the signal and the features for benign overfitting. From a technical perspective, our approach circumvents the traditionally used Convex Gaussian Min-max Theorem (CGMT) by instead leveraging the Dvoretzky-Milman theorem. We emphasize that the FSD method has the potential to refine standard uniform convergence approaches. Furthermore, the isomorphic Dvoretzky-Milman theorem established herein -- proven under the three scenarios mentioned above -- for the $\\ell_q$-norm is of independent mathematical interest.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24350",
  "author_total": 4,
  "authors": [
    {
      "name": "Radosław Adamczak"
    },
    {
      "name": "Guillaume Lecué"
    },
    {
      "name": "Zong Shang"
    },
    {
      "name": "Marta Strzelecka"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/71kk11x6kxpfs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24350",
  "fulltext_url": null,
  "id": "71kk11x6kxpfs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24350",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Statistical Methods and Inference"
    ]
  ],
  "openalex": "W7223037400",
  "pdf_url": "https://arxiv.org/pdf/2610.24350",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/71kk11x6kxpfs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24350",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24350"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Benign Overfitting Property of the Minimum $\\ell_q$ -norm Interpolant Estimator in Regression Problem via Feature Space Decomposition",
  "title_text": "Benign Overfitting Property of the Minimum ℓ_q -norm Interpolant Estimator in Regression Problem via Feature Space Decomposition",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:54Z",
  "url": "https://research.draconitic.com/paper/71kk11x6kxpfs",
  "venue": "arXiv",
  "versions": []
}