B0893
Title: On robustness and local differential privacy
Authors: Thomas Berrett - University of Warwick (United Kingdom) [presenting]
Yi Yu - University of Warwick (United Kingdom)
Mengchu Li - University of Warwick (United Kingdom)
Abstract: It is in 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 knowledge, the focus is on prototype, systematical study of the connections between the optimality under Huber's contamination model and the local differential privacy (LDP) constraints. It started with a general minimax lower bound result, which disentangles the costs of being robust against Huber's contamination and preserving LDP. Four concrete examples are further studied: 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, procedures are demonstrated 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 the connections between robustness and LDP are unveiled via partially answering whether LDP procedures are robust and whether robust procedures can be efficiently privatised. Overall, a promising prospect of joint study is showcased for robustness and local differential privacy.
