{
  "abstract": "We propose a general framework for non-interactive locally differentially private (LDP) learning of structured univariate distributions that can be approximated by piece-wise polynomials. This gives the first sample-efficient LDP learners for several distribution classes, including mixtures of log-concave distributions, such as Gaussian mixture models (GMMs). These learners also provide agnostic guarantees and are computationally efficient. We also prove a lower bound for learning GMMs under LDP, improving on the standard pure-DP packing lower bounds of Bun et al. [BKSW19]. To obtain our general learning framework, we develop an efficient non-interactive LDP algorithm for synthetic data generation over large domains, which may be of independent interest. We then use it together with a deterministic adaptation of the non-private piecewise polynomial learner of Acharya et al. [ADLS17].",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21033",
  "author_total": 3,
  "authors": [
    {
      "name": "Mohammad Afzali"
    },
    {
      "name": "Hassan Ashtiani"
    },
    {
      "name": "Sivan Sabato"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/av9n6n0kkjakj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21033",
  "fulltext_url": null,
  "id": "av9n6n0kkjakj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.21033",
  "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.CR"
    ],
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Privacy-Preserving Technologies in Data"
    ]
  ],
  "openalex": "W7222559022",
  "pdf_url": "https://arxiv.org/pdf/2610.21033",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/av9n6n0kkjakj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21033",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21033"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "Efficient Agnostic Learning of Univariate Densities Under Local Differential Privacy",
  "title_text": "Efficient Agnostic Learning of Univariate Densities Under Local Differential Privacy",
  "type": "preprint",
  "updated_at": "2026-10-30T12:30:00Z",
  "url": "https://research.draconitic.com/paper/av9n6n0kkjakj",
  "venue": "arXiv",
  "versions": []
}