{
  "abstract": "HyperLogLog is a now classic probabilistic algorithm that provides an approximation of the number of distinct elements in a massive dataset, using only one pass over the data. In the original article, Flajolet, Fusy, Gandouet, Meunier (2007) provided a sharp analysis of the expectation and variance of the output, using explicit formulas analyzed using poissonization and Mellin transform. In this short article, we revisit the analysis of HyperLogLog with a more probabilistic viewpoint. This allows us to establish exponential deviation inequalities for the HyperLogLog estimator. The methods are elementary, but the estimates are non-asymptotic and totally explicit.",
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  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.22063",
  "author_total": 1,
  "authors": [
    {
      "name": "Lucas Gerin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4tt34q8wbjy8b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.22063",
  "fulltext_url": null,
  "id": "4tt34q8wbjy8b",
  "issns": [],
  "landing_url": "https://hal.science/hal-05702505v2",
  "language": "en",
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
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  "openalex": "W7171381160",
  "pdf_url": "https://hal.science/hal-05702505/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4tt34q8wbjy8b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:45Z",
      "native_id": "hal-05702505",
      "source": "hal",
      "url": "https://hal.science/hal-05702505v2"
    },
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2607.22063",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.22063"
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  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "HyperLogLog for probabilists",
  "title_text": "HyperLogLog for probabilists",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/4tt34q8wbjy8b",
  "venue": "HAL",
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}