{
  "abstract": "We study the design of a statistical privacy mechanism under a bounded $α$-lift leakage constraint. An agent observes useful data $Y$, which is arbitrarily correlated with private data $X$, and releases $U$. The goal is to maximize Pearson $χ^2$-information $χ^2(Y;U)$ while satisfying the point-wise privacy constraint. This utility is an $f$-information that is nonnegative, obeys data processing, and measures the aggregate normalized change from the prior $P_Y$ to the posteriors $P_{Y|U=u}$. The main benefit of this choice is that $χ^2(Y;U)$ is exactly quadratic in the posterior perturbations; hence, no local approximation of the utility is required. For the nonlinear $α$-lift constraint, we derive a uniform Taylor-remainder bound that remains valid for the optimizing, $ε$-dependent perturbation. When $P_{X|Y}$ is invertible, this yields a closed-form quadratic surrogate, an explicitly scaled binary mechanism that satisfies the original $α$-lift constraint, a computable sufficient range for $ε$, and an $O(ε^{3/2})$ bound on the utility gap. For $α=2$, the solution is exact over an explicit range. We transfer these results to point-wise Rényi-divergence privacy, including an exact-feasible mechanism, an explicit privacy-budget range, and matching gap bounds. We also give an exact formulation for arbitrary leakage matrices and evaluate exact-feasible mechanisms numerically.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13685",
  "author_total": 4,
  "authors": [
    {
      "name": "Amirreza Zamani"
    },
    {
      "name": "Mohammad Amin Zarrabian"
    },
    {
      "name": "Parastoo Sadeghi"
    },
    {
      "name": "Mikael Skoglund"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2fq0jfvqc3aa2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13685",
  "fulltext_url": null,
  "id": "2fq0jfvqc3aa2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13685",
  "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": "W7221531029",
  "pdf_url": "https://arxiv.org/pdf/2610.13685",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2fq0jfvqc3aa2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13685",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13685"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "On Privacy Mechanism Design Under a Bounded $α$-Lift Leakage Constraint with $χ^2$-Utility",
  "title_text": "On Privacy Mechanism Design Under a Bounded α-Lift Leakage Constraint with χ^2-Utility",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/2fq0jfvqc3aa2",
  "venue": "arXiv",
  "versions": []
}