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arXiv 2201.04211cs.CRmath.STstat.TH
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通过矩阵掩码降低差分隐私中的噪声水平

Reducing Noise Level in Differential Privacy through Matrix Masking

A. Adam Ding, Samuel S. Wu, Guanhong Miao, Shigang Chen

AI总结:

本文提出将随机正交矩阵掩码与高斯机制结合,在大数据场景下将实现差分隐私所需的噪声方差从 $O(\ln(1/\delta)/\varepsilon^2)$ 降至 $O(1/\varepsilon)$,从而提升伪数据集的推断准确性并扩大差分隐私的应用范围。

摘要:

近年来,差分隐私方案已被广泛采用以解决数据隐私保护问题。我们提出一种新的高斯方案,并结合另一种数据保护技术——称为随机正交矩阵掩码,以更高效地实现 $(\varepsilon, \delta)$-差分隐私(DP)。我们证明,在大数据环境下,额外的矩阵掩码显著降低了高斯方案实现 $(\varepsilon, \delta)$-DP 所需的噪声方差速率。具体而言,当 $\varepsilon \to 0$,$\delta \to 0$,且样本量 $n$ 超过属性数 $p$ 的幅度为 $(n-p)=O(\ln(1/\delta))$ 时,实现 $(\varepsilon, \delta)$-DP 所需的加性噪声方差从 $O(\ln(1/\delta)/\varepsilon^2)$ 降至 $O(1/\varepsilon)$。由于添加的噪声大大减少,由此得到的差分隐私保护伪数据集能够支持更准确的推断,从而显著扩大差分隐私的适用范围。

英文摘要:

Differential privacy schemes have been widely adopted in recent years to address issues of data privacy protection. We propose a new Gaussian scheme combining with another data protection technique, called random orthogonal matrix masking, to achieve $(\varepsilon, δ)$-differential privacy (DP) more efficiently. We prove that the additional matrix masking significantly reduces the rate of noise variance required in the Gaussian scheme to achieve $(\varepsilon, δ)-$DP in big data setting. Specifically, when $\varepsilon \to 0$, $δ\to 0$, and the sample size $n$ exceeds the number $p$ of attributes by $(n-p)=O(ln(1/δ))$, the required additive noise variance to achieve $(\varepsilon, δ)$-DP is reduced from $O(ln(1/δ)/\varepsilon^2)$ to $O(1/\varepsilon)$. With much less noise added, the resulting differential privacy protected pseudo data sets allow much more accurate inferences, thus can significantly improve the scope of application for differential privacy.

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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