DeepAI AI Chat
Log In Sign Up

On robustness and local differential privacy

by   Mengchu Li, et al.

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's contamination and preserving LDP. We further study three concrete examples: a two-point testing problem, a potentially-diverging mean estimation problem and a nonparametric density 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.


page 1

page 2

page 3

page 4


Minimax optimal goodness-of-fit testing for densities under a local differential privacy constraint

Finding anonymization mechanisms to protect personal data is at the hear...

Adaptive pointwise density estimation under local differential privacy

We consider the estimation of a density at a fixed point under a local d...

The Cost of Privacy: Optimal Rates of Convergence for Parameter Estimation with Differential Privacy

Privacy-preserving data analysis is a rising challenge in contemporary s...

Score Attack: A Lower Bound Technique for Optimal Differentially Private Learning

Achieving optimal statistical performance while ensuring the privacy of ...

L_1 density estimation from privatised data

We revisit the classical problem of nonparametric density estimation, bu...

Pointwise adaptive kernel density estimation under local approximate differential privacy

We consider non-parametric density estimation in the framework of local ...

Breaking the Communication-Privacy-Accuracy Trilemma

Two major challenges in distributed learning and estimation are 1) prese...