Reducing Noise Level in Differential Privacy through Matrix Masking

TL;DR

This paper introduces a matrix masking technique combined with Gaussian noise to enhance differential privacy, significantly reducing noise variance needed and enabling more accurate data analysis in big data contexts.

Contribution

The paper presents a novel matrix masking method that reduces the noise variance in Gaussian differential privacy schemes, improving efficiency and accuracy.

Findings

Reduces noise variance from O(ln(1/δ))/ε^2 to O(1/ε) in big data settings.

Allows more accurate data inference with less added noise.

Enhances the scope of differential privacy applications.

Abstract

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 $(\varepsilon, \delta)$-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 $(\varepsilon, \delta)-$DP in big data setting. Specifically, when $\varepsilon \to 0$, $\delta \to 0$, and the sample size $n$ exceeds the number $p$ of attributes by $(n-p)=O(ln(1/\delta))$, the required additive noise variance to achieve $(\varepsilon, \delta)$-DP is reduced from $O(ln(1/\delta)/\varepsilon^2)$ 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.