OPTT：局部差分隐私下分析数值数据的最优分段变换技术
OPTT: Optimal Piecewise Transformation Technique for Analyzing Numerical Data under Local Differential Privacy
摘要：
隐私保护数据分析（PPDA）由于其广泛的应用而受到越来越多的关注。本地差分隐私（LDP）作为一种适用于PPDA的新兴标准，已被广泛部署到各种现实场景中，用于分析海量数据，同时防止多种形式的隐私泄露。在本研究中，我们主要关注于分析局部差分隐私下数值资料的分段转换技术（PTT）。本文提出了一个基于LDP的PTT原则框架，并在此基础上对PTT进行了系统的研究。结果表明：（1）PTTs中的许多成员在用于获得数值数据均值的无偏估计时是渐近最优的;（2）对于给定的隐私预算，存在达到方差理论下限的PTT.接下来，我们通过详细研究两类PTT来证明：（1）与常用技术相比，不存在最佳PTT，即，Duchi的方案，在一致性噪声方差方面，（2）另一方面，人们有能力找到大量的PTT，这些PTT在最坏情况的噪声方差方面始终比后者更优，这是迄今为止从未报道过的。当我们被限制为只考虑高隐私级别时，足够的PTT比众所周知的拉普拉斯机制更优。最后，我们证明了，对于一个家庭的PTT，相应的噪声方差的理论下界遵循$O(ε^{-2})$时，考虑到高的隐私水平。
英文摘要：
Privacy preserving data analysis (PPDA) has received increasing attention due to a great variety of applications. Local differential privacy (LDP), as an emerging standard that is suitable for PPDA, has been widely deployed into various real-world scenarios to analyze massive data while protecting against many forms of privacy breach. In this study, we are mainly concerned with piecewise transformation technique (PTT) for analyzing numerical data under local differential privacy. We provide a principled framework for PTT in the context of LDP, based on which PTT is studied systematically. As a result, we show that (1) many members in PTTs are asymptotically optimal when used to obtain an unbiased estimator for mean of numerical data, and (2) for a given privacy budget, there is PTT that reaches the theoretical low bound with respect to variance. Next, we prove by studying two classes of PTTs in detail that (1) there do not exist optimal PTTs compared to the well-used technique, i.e., Duchi's scheme, in terms of the consistency noisy variance, (2) on the other hand, one has the ability to find a great number of PTTs that are consistently more optimal than the latter with regard to the worst-case noisy variance, which is never reported so far. When we are restricted to consider only the high privacy level, enough PTTs turn out to be optimal than the well-known Laplace mechanism. Lastly, we prove that for a family of PTTs, the correspondingly theoretical low bound of noisy variance follows $O(ε^{-2})$ when considering the high privacy level.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
