This paper introduces a relaxed noise calibration method to enhance data utility while attaining pufferfish privacy. This work builds on the existing $1$-Wasserstein (Kantorovich) mechanism by alleviating the existing overly strict condition that leads to excessive noise, and proposes a practical mechanism design algorithm as a general solution. We prove that a strict noise reduction by our approach always exists compared to $1$-Wasserstein mechanism for all privacy budgets $ε$ and prior beliefs, and the noise reduction (also represents improvement on data utility) gains increase significantly for low privacy budget situations--which are commonly seen in real-world deployments. We also analyze the variation and optimality of the noise reduction with different prior distributions. Moreover, all the properties of the noise reduction still exist in the worst-case $1$-Wasserstein mechanism we introduced, when the additive noise is largest. We further show that the worst-case $1$-Wasserstein mechanism is equivalent to the $\ell_1$-sensitivity method. Experimental results on three real-world datasets demonstrate $47\%$ to $87\%$ improvement in data utility.

翻译：本文提出一种松弛的噪声校准方法，在实现河豚隐私的同时提升数据效用。本工作基于现有的1-瓦瑟斯坦（康托罗维奇）机制，通过缓解原有导致过度噪声的严苛条件，提出一种实用的机制设计算法作为通用解决方案。我们证明，相较于1-瓦瑟斯坦机制，在所有隐私预算ε和先验信念下，本方法始终存在严格的噪声削减，且在低隐私预算场景（实际部署中常见）中噪声削减量（即数据效用提升幅度）显著增加。我们还分析了不同先验分布下噪声削减的变化规律与最优性。此外，当我们引入的加性噪声达到最大时，所有噪声削减特性在最坏情况1-瓦瑟斯坦机制中依然成立。我们进一步证明最坏情况1-瓦瑟斯坦机制等价于ℓ1-敏感度方法。在三个真实数据集上的实验结果表明，数据效用提升了47%至87%。