Uniformity Testing in the Shuffle Model: Simpler, Better, Faster

TL;DR

This paper simplifies the analysis of uniformity testing algorithms in the shuffle model of differential privacy, providing more accessible and efficient methods while maintaining strong privacy guarantees.

Contribution

It offers a simplified, more elementary analysis of existing algorithms and introduces an alternative approach leveraging privacy amplification via shuffling.

Findings

Simplified analysis of uniformity testing in the shuffle model

An alternative algorithm with comparable guarantees

Elementary and streamlined proof techniques

Abstract

Uniformity testing, or testing whether independent observations are uniformly distributed, is the prototypical question in distribution testing. Over the past years, a line of work has been focusing on uniformity testing under privacy constraints on the data, and obtained private and data-efficient algorithms under various privacy models such as central differential privacy (DP), local privacy (LDP), pan-privacy, and, very recently, the shuffle model of differential privacy. In this work, we considerably simplify the analysis of the known uniformity testing algorithm in the shuffle model, and, using a recent result on "privacy amplification via shuffling," provide an alternative algorithm attaining the same guarantees with an elementary and streamlined argument.