COINPRESS: PRACTICAL PRIVATE POINT ESTIMATION AND CONFIDENCE INTERVALS

GAUTAM  KAMATH – UNIVERSITY OF WATERLOO

ABSTRACT

We consider point estimation and generation of confidence intervals under the constraint of differential privacy. We provide a simple and practical framework for these tasks in relatively general settings. Our investigation addresses a novel challenge that arises in the differentially private setting, which involves the cost of weak a priori bounds on the parameters of interest. This framework is applied to the problems of Gaussian mean and covariance estimation. Despite the simplicity of our method, we are able to achieve minimax near-optimal rates for these problems. Empirical evaluations, on the problems of mean estimation, covariance estimation, and principal component analysis, demonstrate significant improvements in comparison to previous work.

No knowledge of differential privacy will be assumed. Based on joint works with Sourav Biswas, Yihe Dong, Jerry Li, Vikrant Singhal, and Jonathan Ullman.