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This paper investigates the utility gain of using Iterative Bayesian Update(IBU) for private discrete distribution estimation using data obfuscated withLocally Differentially Private (LDP) mechanisms. We compare the performance ofIBU to Matrix Inversion (MI), a standard estimation technique, for seven LDPmechanisms designed for one-time data collection and for other seven LDPmechanisms designed for multiple data collections (e.g., RAPPOR). To broadenthe scope of our study, we also varied the utility metric, the number of usersn, the domain size k, and the privacy parameter {\epsilon}, using bothsynthetic and real-world data. Our results suggest that IBU can be a usefulpost-processing tool for improving the utility of LDP mechanisms in differentscenarios without any additional privacy cost. For instance, our experimentsshow that IBU can provide better utility than MI, especially in high privacyregimes (i.e., when {\epsilon} is small). Our paper provides insights forpractitioners to use IBU in conjunction with existing LDP mechanisms for moreaccurate and privacy-preserving data analysis. Finally, we implemented IBU forall fourteen LDP mechanisms into the state-of-the-art multi-freq-ldpy Pythonpackage (https://pypi.org/project/multi-freq-ldpy/) and open-sourced all ourcode used for the experiments as tutorials.

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