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.

本研究基于不同的单次数据采集和多次数据采集的LDP机制，比较了使用迭代贝叶斯更新（IBU）和矩阵反演（MI）两种不同技术进行隐私离散分布估计的效果。研究结果表明，IBU可以在不增加额外隐私成本的情况下，提高不同场景下LDP机制的效用，尤其是在高隐私环境下更为明显。

关于局部差分隐私机制迭代贝叶斯更新的效用增益