{
  "abstract": "Information-theoretic generalization bounds usually control dependence on the task sample, whereas selective privacy may constrain only a different, private coordinate. We study i.i.d. pairs $(X,Y)$, where a learner observes $(X^n,Y^n)$, leaks at most $ε_n$ nats about $X^n$, and incurs loss on $Y$. A chain-rule transfer converts this mismatched constraint into the closed-form universal certificate $I(W;Y^n)\\leq\\min\\{nH(Y),nH(Y\\mid X)+ε_n\\}$. Combining the certificate with mutual-information generalization yields a bound governed by residual task uncertainty and normalized privacy leakage. We derive complementary task-compression and individual-sample refinements, identify a sharp obstruction showing why selective privacy alone need not give a vanishing certificate, and invert the bound to obtain the exact leakage allowance for a prescribed generalization tolerance. We prove exact information-level achievability for deterministic-task and independent-residual source families and show that the resulting $\\sqrt{ε_n/n}$ generalization rate is tight up to a universal constant. We also give a fixed-horizon adaptive application in which conditional leakage costs add.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15847",
  "author_total": 3,
  "authors": [
    {
      "name": "Amirreza Zamani"
    },
    {
      "name": "Parastoo Sadeghi"
    },
    {
      "name": "Mikael Skoglund"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6jgjnkx52naqf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15847",
  "fulltext_url": null,
  "id": "6jgjnkx52naqf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15847",
  "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.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "openalex",
      "1702|Privacy-Preserving Technologies in Data"
    ]
  ],
  "openalex": "W7221754470",
  "pdf_url": "https://arxiv.org/pdf/2610.15847",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6jgjnkx52naqf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15847",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15847"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "Residual-Information Generalization Bounds Under Selective Privacy: Extended Version",
  "title_text": "Residual-Information Generalization Bounds Under Selective Privacy: Extended Version",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/6jgjnkx52naqf",
  "venue": "arXiv",
  "versions": []
}