On robustness and local differential privacy
本文首次系统研究Huber污染模型下的最优性与局部差分隐私约束之间的联系，通过一般极小化下界和四个具体例子（两点检验、均值估计、密度估计、中位数估计）展示了同时应对污染和隐私约束的最优方法，并探讨了稳健性与LDP之间的相互影响。
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 differential 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 preserving 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.