A Utility-Optimized Framework for Personalized Private Histogram Estimation

Recently, local differential privacy (LDP), as a strong and practical notion, has been applied to deal with privacy issues in data collection. However, existing LDP-based strategies mainly focus on utility optimization at a single privacy level while ignoring various privacy preferences of data providers and multilevel privacy demands for statistics. In this paper, we for the first time propose a framework to optimize the utility of histogram estimation with these two privacy requirements. To clarify the goal of privacy protection, we personalize the traditional definition of LDP. We design two independent approaches to minimize the utility loss: Advanced Combination, which composes multilevel results for utility optimization, and Data Recycle with Personalized Privacy, which enlarges the sample size for an estimation. We demonstrate their effectiveness on privacy and utility, respectively. Moreover, we embed these approaches within a Recycle and Combination Framework and prove that the framework stably achieves the optimal utility by quantifying its error bounds. On real-world datasets, our approaches are experimentally validated and remarkably outperform baseline methods.