Analysis of differentially private synthetic data: a general measurement error approach

Yangdi Jiang, Yi Liu, Xiaodong Yan, Anne-Sophie Charest, Linglong Kong, Bei Jiang

Keywords: Measurement Error Model, Differential Privacy, Regression, Statistical Inference

Abstract: Differential private (DP) synthetic datasets have been receiving significant attention from academia, industry, and government. However, little is known about how to perform statistical inference using DP synthetic datasets. Naive approaches that do not take into account the induced uncertainty due to DP mechanism will result in biased estimators and invalid inferences. In this paper, we present a general class of bias-corrected DP estimators with valid asymptotic confidence intervals for parameters in regression settings, by establishing the connection between additive DP mechanisms and measurement error models. Our simulation shows that when the sample covariance between DP noises and data is close to zero, our estimator is far superior to the widely used sufficient statistic perturbation algorithm, and the CIs can achieve better coverage when comparing to the naive CIs obtained from ignoring the DP mechanism.

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