ON ROBUSTNESS AND LOCAL DIFFERENTIAL PRIVACY

• 成果类型: Article
• 署名作者: Li, Mengchu; Berrett, Thomas B.; Yu, Yi
• 署名单位: University of Warwick
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/23-AOS2267
• 发表日期: 2023
• 页码: 717-737
• 关键词: geometrizing rates; estimators; CONVERGENCE

摘要

It is of soaring demand to develop statistical analysis tools that are robust against contamination as well as preserving individual data owners' privacy. In spite of the fact that both topics host a rich body of literature, to the best of our knowledge, we are the first to systematically study the connections between the optimality under Huber's contamination model and the local dif-ferential privacy (LDP) constraints.In this paper, we start with a general minimax lower bound result, which disentangles the costs of being robust against Huber contamination and pre-serving LDP. We further study four concrete examples: a two-point testing problem, a potentially diverging mean estimation problem, a nonparametric density estimation problem and a univariate median estimation problem. For each problem, we demonstrate procedures that are optimal in the presence of both contamination and LDP constraints, comment on the connections with the state-of-the-art methods that are only studied under either contamination or privacy constraints, and unveil the connections between robustness and LDP via partially answering whether LDP procedures are robust and whether robust procedures can be efficiently privatised. Overall, our work showcases a promising prospect of joint study for robustness and local differential privacy.