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

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