Statistical Properties of Sanitized Results from Differentially Private Laplace Mechanisms with Noninformative Bounding
Fang Liu · arXiv (Cornell University) · 2016
Protection of individual privacy is a common concern when releasing and sharing data and information. Differential privacy (DP) formalizes privacy in probabilistic terms without making assumptions about the background knowledge of data intruders, and thus provides a robust concept for privacy protection. Practical applications of DP involve development of differentially private mechanisms to generate sanitized results at a pre-specified privacy budget. In the sanitization of bounded statistics such as proportions and correlation coefficients, the bounding constraints will need to be incorporated in the differentially private mechanisms. There has been little work in examining the consequences of the incorporation of of bounding constraints on the accuracy of sanitized results from a differentially private mechanism. In this paper, we define noninformative and informative bounding procedures in the sanitization of bounded data, depending on whether a bounding procedure itself leaks original information or not. We formalize the differentially private truncated and boundary inflated truncated (BIT) mechanisms that release bounded statistics. The impacts of the noninformative truncated and BIT mechanisms on the statistical validity of sanitized statistics, including bias and consistency, in the framework of the Laplace mechanism are evaluated both theoretically and empirically via simulation studies.