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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

Chinese

本论文得出一个通过随机响应实现的差异性隐私下多变交叉的准确减缓公式。从符合差异性隐私保证的随机化矩阵的建议的替代公式中,我们表明,在属性水平的随机化下,并且整个分布的随机化是由Kronecker产品特征的,涉及不同属性的匿名数据集的任何交叉点等于由减缓参数倍增的原始交叉点,由每个属性分配的整体隐私预算的部分自行决定。

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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