On the Utility Gain of Iterative Bayesian Update for Locally Differentially Private Mechanisms

TL;DR

This paper demonstrates that Iterative Bayesian Update (IBU) enhances the utility of locally differentially private mechanisms for discrete distribution estimation, especially in high privacy regimes, without additional privacy loss.

Contribution

It introduces the use of IBU as a post-processing step for LDP mechanisms, showing improved utility over traditional methods across various scenarios and data types.

Findings

IBU outperforms Matrix Inversion in high privacy regimes.

IBU improves utility for multiple LDP mechanisms without extra privacy cost.

The authors provide an open-source implementation and tutorials for practical use.

Abstract

This paper investigates the utility gain of using Iterative Bayesian Update (IBU) for private discrete distribution estimation using data obfuscated with Locally Differentially Private (LDP) mechanisms. We compare the performance of IBU to Matrix Inversion (MI), a standard estimation technique, for seven LDP mechanisms designed for one-time data collection and for other seven LDP mechanisms designed for multiple data collections (e.g., RAPPOR). To broaden the scope of our study, we also varied the utility metric, the number of users n, the domain size k, and the privacy parameter {\epsilon}, using both synthetic and real-world data. Our results suggest that IBU can be a useful post-processing tool for improving the utility of LDP mechanisms in different scenarios without any additional privacy cost. For instance, our experiments show that IBU can provide better utility than MI, especially in high privacy regimes (i.e., when {\epsilon} is small). Our paper provides insights for practitioners to use IBU in conjunction with existing LDP mechanisms for more accurate and privacy-preserving data analysis. Finally, we implemented IBU for all fourteen LDP mechanisms into the state-of-the-art multi-freq-ldpy Python package (https://pypi.org/project/multi-freq-ldpy/) and open-sourced all our code used for the experiments as tutorials.