Uniformity Testing under User-Level Local Privacy

TL;DR

This paper studies the problem of testing whether a distribution is uniform under user-level local differential privacy, proposing nearly optimal algorithms that work without shared randomness or global identifiers.

Contribution

It introduces the first nearly optimal algorithms for uniformity and identity testing under user-level local differential privacy, a significantly more challenging setting than standard local privacy.

Findings

Developed nearly sample-optimal algorithms for user-level LDP testing.

Focused on the private-coin, symmetric setting without shared randomness.

Addressed a fundamental gap in distribution testing under user-level privacy.

Abstract

We initiate the study of distribution testing under \emph{user-level} local differential privacy, where each of $n$ users contributes $m$ samples from the unknown underlying distribution. This setting, albeit very natural, is significantly more challenging that the usual locally private setting, as for the same parameter $\varepsilon$ the privacy guarantee must now apply to a full batch of $m$ data points. While some recent work consider distribution \emph{learning} in this user-level setting, nothing was known for even the most fundamental testing task, uniformity testing (and its generalization, identity testing). We address this gap, by providing (nearly) sample-optimal user-level LDP algorithms for uniformity and identity testing. Motivated by practical considerations, our main focus is on the private-coin, symmetric setting, which does not require users to share a common random seed nor to have been assigned a globally unique identifier.