Uniformity Testing under User-Level Local Privacy

2025-10-21

AI Summary

This paper investigates uniformity and identity testing under user-level local differential privacy (LDP), where each user contributes multiple independent samples from an unknown distribution, subject to stringent privacy constraints. Addressing the absence of foundational testing theory for this setting, we propose the first unified testing framework for user-level LDP: leveraging a symmetric private-coin protocol, we design sampling and testing algorithms that require no public randomness, global identifiers, or trusted central servers, while achieving near-optimal statistical performance. Our theoretical analysis establishes that the proposed methods attain sample complexity approaching the information-theoretic lower bound, ensuring optimal statistical power under strong privacy guarantees. This work fills a critical theoretical gap in distribution testing under user-level LDP and provides a lightweight, deployable statistical testing tool for privacy-preserving data publishing and federated analytics.

Technology Category

• Machine Learning: Privacy
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Local Search

Application Category

• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Responsible Web: Data and user privacy-enhancing technologies for the Web

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.

Problem

• Testing uniformity under user-level local privacy constraints
• Addressing distribution testing with multiple samples per user
• Developing private-coin symmetric algorithms for identity testing

Innovation

• User-level local differential privacy for distribution testing
• Private-coin symmetric setting without shared randomness
• Sample-optimal algorithms for uniformity and identity testing