{
  "abstract": "We study the possibility of generalizing maximum-entropy reconstruction, which approximately recovers a probability distribution from finitely many (generalized) moments by minimizing the Kullback--Leibler (KL) divergence to a reference measure. The reconstruction lies in an exponential family and is also the best KL approximation of the unknown distribution within that family: moment matching and information projection coincide. Replacing KL by a smooth f-divergence, the reconstruction still exists in an associated family, but the best approximation property does not. Specifically, a family is called entropy-adapted if the projection of any distribution matches its moments. We show that, up to equivalence, KL is the only $C^2$ f-divergence that is entropy-adapted, whatever the choice of the generalized moments. We illustrate the consequences of this failure numerically.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.21872",
  "author_total": 3,
  "authors": [
    {
      "name": "Justin Bec"
    },
    {
      "name": "Thomas Le Corre"
    },
    {
      "name": "Aurélien Garivier"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/78h9cwatphbxa.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.21872",
  "fulltext_url": null,
  "id": "78h9cwatphbxa",
  "issns": [],
  "landing_url": "https://hal.science/hal-05802905v1",
  "language": "en",
  "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": [
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      "arxiv",
      "cs.IT"
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      "arxiv",
      "math.ST"
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    [
      "openalex",
      "3109|Statistical Mechanics and Entropy"
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  ],
  "openalex": "W7222588830",
  "pdf_url": "https://arxiv.org/pdf/2610.21872",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/78h9cwatphbxa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:58Z",
      "native_id": "hal-05802905",
      "source": "hal",
      "url": "https://hal.science/hal-05802905v1"
    },
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.21872",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.21872"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "On Minimum Divergence for Distribution Reconstruction",
  "title_text": "On Minimum Divergence for Distribution Reconstruction",
  "type": "preprint",
  "updated_at": "2026-10-30T12:30:00Z",
  "url": "https://research.draconitic.com/paper/78h9cwatphbxa",
  "venue": "HAL",
  "versions": []
}