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Differential privacy with adjustable preservation of multivariate relationships

Nicolas Ruiz · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.26460 · cited by 0 works (OpenAlex) · open-access PDF

Japanese

この論文は、ランダムな応答によって達成された差異的なプライバシーにおける多様な交差点のための正確な減少式を生み出します。差異的なプライバシー保証に準拠するランダム化マトリックスの提案の代替式から、我々は、属性レベルのランダム化の下で、および全体の分布のランダム化がクロネッカー製品によって特徴付けられている場合、異なる属性を含む匿名化されたデータセットのすべての交差点は、減少パラメータによって倍増した原始の交差点に等しいことを示します。この特徴化は、各属性に割り当てられた全体的なプライバシー予算の部分によって決定されます。この特徴化は、差異的なプライバシー

Machine translation (Meta M2M100); the English original follows.

Abstract

This paper derives an exact attenuation formula for multivariate cross-moments under differential privacy achieved through randomized response. From a proposed alternative formulation of randomization matrices compliant with differential privacy guarantees we show that, under attribute-level randomization and where the randomization of the whole distribution is characterized by Kronecker products, any cross-moment of the anonymized dataset involving distinct attributes is equal to the original cross-moment multiplied by attenuation parameters, themselves determined by the part of the overall privacy budget allocated to each attribute. This characterization enables explicit and transparent controls of multivariate relationships preservations in differential privacy through privacy budget allocation. A simple numerical illustration demonstrates that identical total budgets can yield substantially different covariance-preservation profiles. The results also make the multiplicative loss of higher-order interactions explicit and thus can support mechanism design guided by analytical priorities.

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Topics: Differential privacy, Multivariate statistics, Multiplicative function, Randomized response, Kronecker product, Differential (mechanical device)

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