Achieving Differential Privacy with Matrix Masking in Big Data
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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 (ε, 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 (ε, δ)-DP in big data setting. Specifically, when ε→ 0, δ→ 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 (ε, δ)-DP is reduced from O(ln(1/δ)/ε^2) to O(1/ε). 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.
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