Inference under Information Constraints III: Local Privacy Constraints
Abstract
We study goodness-of-fit and independence testing of discrete distributions in a setting where samples are distributed across multiple users. The users wish to preserve the privacy of their data while enabling a central server to perform the tests. Under the notion of local differential privacy, we propose simple, sample-optimal, and communication-efficient protocols for these two questions in the noninteractive setting, where in addition users may or may not share a common random seed. In particular, we show that the availability of shared (public) randomness greatly reduces the sample complexity. Underlying our public-coin protocols are privacy-preserving mappings which, when applied to the samples, minimally contract the distance between their respective probability distributions.
Cite
@article{arxiv.2101.07981,
title = {Inference under Information Constraints III: Local Privacy Constraints},
author = {Jayadev Acharya and Clément L. Canonne and Cody Freitag and Ziteng Sun and Himanshu Tyagi},
journal= {arXiv preprint arXiv:2101.07981},
year = {2021}
}
Comments
To appear in the Special Issue on Privacy and Security of Information Systems of the IEEE Journal on Selected Areas in Information Theory (JSAIT), 2021. Journal version of the AISTATS'19 paper "Test without Trust: Optimal Locally Private Distribution Testing" (arXiv:1808.02174), which it extends and supersedes