This paper investigates lift, the likelihood ratio between the posterior and prior belief about sensitive features in a dataset. Maximum and minimum lifts over sensitive features quantify the adversary's knowledge gain and should be bounded to protect privacy. We demonstrate that max and min lifts have a distinct range of values and probability of appearance in the dataset, referred to as \emph{lift asymmetry}. We propose asymmetric local information privacy (ALIP) as a compatible privacy notion with lift asymmetry, where different bounds can be applied to min and max lifts. We use ALIP in the watchdog and optimal random response (ORR) mechanisms, the main methods to achieve lift-based privacy. It is shown that ALIP enhances utility in these methods compared to existing local information privacy, which ensures the same (symmetric) bounds on both max and min lifts. We propose subset merging for the watchdog mechanism to improve data utility and subset random response for the ORR to reduce complexity. We then investigate the related lift-based measures, including $\ell_1$-norm, $\chi^2$-privacy criterion, and $\alpha$-lift. We reveal that they can only restrict max-lift, resulting in significant min-lift leakage. To overcome this problem, we propose corresponding lift-inverse measures to restrict the min-lift. We apply these lift-based and lift-inverse measures in the watchdog mechanism. We show that they can be considered as relaxations of ALIP, where a higher utility can be achieved by bounding only average max and min lifts.

翻译：本文研究提升（lift），即数据集中敏感特征的先验与后验信念之间的似然比。敏感特征上的最大与最小提升量化了攻击者的知识增益，应加以约束以保护隐私。我们证明最大和最小提升具有不同的取值范围及在数据集中的出现概率，这被称为\emph{提升不对称性}。我们提出非对称局部信息隐私（ALIP）作为与提升不对称性兼容的隐私概念，可对最小和最大提升施加不同约束。我们在看门狗机制和最优随机响应（ORR）机制中使用ALIP，这两种机制是实现基于提升的隐私的主要方法。结果表明，与现有局部信息隐私（对最大和最小提升施加相同对称约束）相比，ALIP在这些方法中提升了效用。我们提出看门狗机制的子集合并以改善数据效用，以及ORR的子集随机响应以降低复杂度。随后，我们研究相关的基于提升的度量，包括$\ell_1$范数、$\chi^2$隐私准则和$\alpha$-提升。我们发现这些度量只能约束最大提升，导致显著的最小提升泄漏。为解决此问题，我们提出相应的提升逆度量以约束最小提升。我们将这些基于提升和提升逆的度量应用于看门狗机制，表明它们可视为ALIP的松弛形式，通过仅约束平均最大和最小提升实现更高效用。