# Statistical Properties of Sanitized Results from Differentially Private Laplace Mechanism with Univariate Bounding Constraints

arXiv: https://arxiv.org/abs/1607.08554 · HTML: https://mlsanity.com/paper/1607.08554/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jul 2016.

## Built on by (most cited first, 4 of 4)

- [Can Querying for Bias Leak Protected Attributes? Achieving Privacy With Smooth Sensitivity](https://mlsanity.com/paper/2211.02139/) (2022)
- [A Differentially Private Weighted Empirical Risk Minimization Procedure and its Application to Outcome Weighted Learning](https://mlsanity.com/paper/2307.13127/) (2023)
- [Provable Privacy with Non-Private Pre-Processing](https://mlsanity.com/paper/2403.13041/) (2024)
- [DPpack: An R Package for Differentially Private Statistical Analysis and Machine Learning](https://mlsanity.com/paper/2309.10965/) (2023)

## Abstract (arXiv)

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.