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    "story_id": "mp-2026-10-25-013",
    "source_story_id": "tmp-story-person-level-private-distributions",
    "edition_id": "mp-2026-10-25-morning-0107",
    "edition_url": "https://themachinepress.com/edition/2026-10-25",
    "position": 13,
    "story_type": "dispatch",
    "section": "safety-security",
    "editorial_classification": "editorial",
    "headline": "Privacy Counts the Person, Not Each Sample",
    "slug": "privacy-counts-the-person-not-each-sample",
    "dek": "A degree-six sum-of-squares estimator reaches near-optimal user counts when every participant contributes a batch from one discrete distribution.",
    "summary": "A degree-six sum-of-squares estimator reaches near-optimal user counts when every participant contributes a batch from one discrete distribution.",
    "body_text": "Sample-level privacy can understate exposure when one person contributes many correlated records. This work studies person-level differential privacy for learning a discrete distribution from n users, each supplying m independent samples. It gives polynomial-time algorithms for both pure and approximate privacy, with the pure-DP user requirement matching the information-theoretic optimum up to logarithmic factors. The construction uses a degree-six sum-of-squares estimator for untrusted batches and a covariance certificate that preserves mean-dependent multinomial variance. A statistical-query lower bound rules out uniformly smaller error under fixed polynomial resources. These are theoretical rate and complexity results under the stated distributional assumptions, not a turnkey privacy guarantee for arbitrary behavioral datasets.",
    "why_it_matters": "A degree-six sum-of-squares estimator reaches near-optimal user counts when every participant contributes a batch from one discrete distribution.",
    "limitations": [
      "These are theoretical rate and complexity results under the stated distributional assumptions, not a turnkey privacy guarantee for arbitrary behavioral datasets."
    ],
    "importance": 9,
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    "first_published_at": "2026-10-25T09:00:00.000-04:00",
    "modified_at": "2026-10-25T09:00:00.000-04:00",
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        "text": "A degree-six sum-of-squares estimator reaches near-optimal user counts when every participant contributes a batch from one discrete distribution.",
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        "qualification": "These are theoretical rate and complexity results under the stated distributional assumptions, not a turnkey privacy guarantee for arbitrary behavioral datasets."
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    "source_ids": [
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    "tags": [
      "differential privacy",
      "distribution learning",
      "robust statistics",
      "theory"
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    "image_url": "https://themachinepress.com/issues/2026-10-25/person-privacy-scales.webp",
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  "sources": [
    {
      "source_id": "source-2026-10-25-013",
      "title": "arXiv preprint 2610.31612, original v1",
      "publisher": "arXiv",
      "url": "https://arxiv.org/abs/2610.31612v1",
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      "source_type": "primary_research",
      "is_primary_source": true,
      "published_at": "2026-10-22T13:40:13.000-04:00",
      "accessed_at": "2026-10-25T08:17:14.361-04:00",
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  "publisher": {
    "name": "The Machine Press",
    "url": "https://themachinepress.com",
    "description": "A daily newspaper for the age of artificial intelligence."
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  "cite_this_report": {
    "title": "Privacy Counts the Person, Not Each Sample",
    "publisher": "The Machine Press",
    "published_at": "2026-10-25T09:00:00.000-04:00",
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