Xingyuan Zhao

Xingyuan Zhao, Ruyu Zhou, Fang Liu

Applying a randomized algorithm to a subset rather than the entire dataset amplifies privacy guarantees. We propose a class of subsampling methods ``MUltistage Sampling Technique (MUST)'' for privacy amplification (PA) in the context of differential privacy (DP). We conduct comprehensive analyses of the PA effects and utility for several 2-stage MUST procedures through newly introduced concept including strong vs weak PA effects and aligned privacy profile. We provide the privacy loss composition analysis over repeated applications of MUST via the Fourier accountant algorithm. Our theoretical and empirical results suggest that MUST offers stronger PA in $ε$ than the common one-stage sampling procedures including Poisson sampling, sampling without replacement, and sampling with replacement, while the results on $δ$ vary case by case. Our experiments show that MUST is non-inferior in the utility and stability of privacy-preserving (PP) outputs to one-stage subsampling methods at similar privacy loss while enhancing the computational efficiency of algorithms that require complex function calculations on distinct data points. MUST can be seamlessly integrated into stochastic optimization algorithms or procedures that involve parallel or simultaneous subsampling when DP guarantees are necessary.

Fang Liu, Xingyuan Zhao

Differential privacy (DP) provides a robust model to achieve privacy guarantees for released information. We examine the protection potency of sanitized multi-dimensional frequency distributions via DP randomization mechanisms against homogeneity attack (HA). HA allows adversaries to obtain the exact values on sensitive attributes for their targets without having to identify them from the released data. We propose measures for disclosure risk from HA and derive closed-form relationships between the privacy loss parameters in DP and the disclosure risk from HA. The availability of the closed-form relationships assists understanding the abstract concepts of DP and privacy loss parameters by putting them in the context of a concrete privacy attack and offers a perspective for choosing privacy loss parameters when employing DP mechanisms in information sanitization and release in practice. We apply the closed-form mathematical relationships in real-life datasets to demonstrate the assessment of disclosure risk due to HA on differentially private sanitized frequency distributions at various privacy loss parameters.