Reducing Noise Level in Differential Privacy through Matrix Masking
This work addresses the challenge of balancing privacy and utility in big data settings for data analysts and practitioners, representing an incremental improvement over existing methods.
The paper tackles the problem of high noise levels in differential privacy by proposing a Gaussian scheme combined with random orthogonal matrix masking, which reduces the required noise variance from O(ln(1/δ)/ε²) to O(1/ε) under specific conditions, enabling more accurate inferences.
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.