Inference under Information Constraints III: Local Privacy Constraints

TL;DR

This paper develops optimal local differential privacy protocols for goodness-of-fit and independence testing of discrete distributions, demonstrating how shared randomness reduces sample complexity while preserving privacy.

Contribution

It introduces simple, sample-optimal, communication-efficient protocols for distribution testing under local privacy constraints, highlighting the impact of shared randomness.

Findings

Shared randomness significantly reduces sample complexity.

Protocols are simple, sample-optimal, and communication-efficient.

Privacy-preserving mappings minimally contract distribution distances.

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.