Nonparametric extensions of randomized response for private confidence sets

arXiv2202.08728MaRDI QIDQ6391410

Author name not available (Why is that?)

Publication date: 17 February 2022

Abstract: This work derives methods for performing nonparametric, nonasymptotic statistical inference for population means under the constraint of local differential privacy (LDP). Given bounded observations $(X_1,dots,X_n)$ with mean $m{u}^{s}tar$ that are privatized into $(Z_1,dots,Z_n)$, we present confidence intervals (CI) and time-uniform confidence sequences (CS) for $m{u}^{s}tar$ when only given access to the privatized data. To achieve this, we introduce a nonparametric and sequentially interactive generalization of Warner's famous ``randomized response mechanism, satisfying LDP for arbitrary bounded random variables, and then provide CIs and CSs for their means given access to the resulting privatized observations. For example, our results yield private analogues of Hoeffding's inequality in both fixed-time and time-uniform regimes. We extend these Hoeffding-type CSs to capture time-varying (non-stationary) means, and conclude by illustrating how these methods can be used to conduct private online A/B tests.

Has companion code repository: https://github.com/wannabesmith/nprr

This page was built for publication: Nonparametric extensions of randomized response for private confidence sets

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6391410)