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arXiv 2304.04410cs.CR
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本地与Shuffle模型中的差分隐私数值向量分析

Differentially Private Numerical Vector Analyses in the Local and Shuffle Model

Shaowei Wang, Jin Li, Yuntong Li, Jin Li, Wei Yang, Hongyang Yan

AI总结:

本研究针对本地差分隐私下的数值向量聚合,提出最优的Collision与CoCo机制以降低估计误差,并在Shuffle模型中推导出精确的隐私放大界限,显著减少了频率与均值估计误差。

摘要:

数值向量聚合在隐私敏感应用中起着至关重要的作用,例如联邦学习中的分布式梯度估计和键值数据的统计分析。在本地差分隐私的背景下,本研究提供了紧致的极小化极大误差界$O(\ rac{ds}{nε^2})$,其中$d$表示数值向量的维度,$s$表示非零项的数量。通过将条件/无条件数值均值估计问题转化为频率估计问题,我们开发了一种名为Collision的最优且高效的机制。相比之下,现有方法表现出次优的误差率$O(\ rac{d^2}{nε^2})$或$O(\ rac{ds^2}{nε^2})$。具体而言,对于无条件均值估计,我们利用每个维度中两个频率之间的负相关性,提出了CoCo机制,与Collision相比,该机制进一步减少了均值的估计误差。此外,为了突破本地隐私中的误差障碍,我们在Shuffle模型中检验了所提机制的隐私放大效应,并推导出了精确紧致的放大界限。我们的实验验证了我们的机制并与现有方法进行了比较,证明了在数值向量的频率估计和均值估计方面误差显著减少。

英文摘要:

Numerical vector aggregation plays a crucial role in privacy-sensitive applications, such as distributed gradient estimation in federated learning and statistical analysis of key-value data. In the context of local differential privacy, this study provides a tight minimax error bound of $O(\frac{ds}{nε^2})$, where $d$ represents the dimension of the numerical vector and $s$ denotes the number of non-zero entries. By converting the conditional/unconditional numerical mean estimation problem into a frequency estimation problem, we develop an optimal and efficient mechanism called Collision. In contrast, existing methods exhibit sub-optimal error rates of $O(\frac{d^2}{nε^2})$ or $O(\frac{ds^2}{nε^2})$. Specifically, for unconditional mean estimation, we leverage the negative correlation between two frequencies in each dimension and propose the CoCo mechanism, which further reduces estimation errors for mean values compared to Collision. Moreover, to surpass the error barrier in local privacy, we examine privacy amplification in the shuffle model for the proposed mechanisms and derive precisely tight amplification bounds. Our experiments validate and compare our mechanisms with existing approaches, demonstrating significant error reductions for frequency estimation and mean estimation on numerical vectors.

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。

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