Statistical Properties of Sanitized Results from Differentially Private Laplace Mechanism with Univariate Bounding Constraints
This work addresses privacy concerns for data analysts releasing bounded statistics, but it is incremental as it builds on existing differential privacy mechanisms by incorporating known constraints.
The paper tackles the problem of maintaining statistical accuracy when applying differential privacy to bounded statistics like proportions, by formalizing truncated and boundary inflated truncated Laplace procedures. The result includes theoretical and empirical evaluations showing how these constraints affect the accuracy and validity of sanitized results, with specific numerical insights from simulations.
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. For the sanitization of statistics with publicly known bounds such as proportions and correlation coefficients, the bounding constraints will need to be incorporated in the differentially private mechanisms. There has been little work on examining the consequences of the bounding constraints on the accuracy of sanitized results and the statistical inferences of the population parameters based on the sanitized results. In this paper, we formalize the differentially private truncated and boundary inflated truncated (BIT) procedures for releasing statistics with publicly known bounding constraints. The impacts of the truncated and BIT Laplace procedures on the statistical accuracy and validity of sanitized statistics are evaluated both theoretically and empirically via simulation studies.