Better Private Distribution Testing by Leveraging Unverified Auxiliary Data

2025-03-18

AI Summary

This work studies distribution testing under differential privacy, leveraging unreliable yet publicly available auxiliary prior information to improve statistical efficiency—specifically for uniformity, identity, and closeness testing. We propose the first differentially private *enhanced* distribution testing framework and design optimal, adaptive algorithms whose sample complexity smoothly decreases with the quality of the auxiliary prior, achieving (up to logarithmic factors) minimax-optimal sample complexity under given privacy budgets. We further establish matching information-theoretic lower bounds. Theoretically and empirically, our approach significantly reduces the privacy cost when high-quality auxiliary information is available, marking the first method that jointly optimizes auxiliary prior utilization and differential privacy constraints.

Technology Category

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

Application Category

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

Abstract

We extend the framework of augmented distribution testing (Aliakbarpour, Indyk, Rubinfeld, and Silwal, NeurIPS 2024) to the differentially private setting. This captures scenarios where a data analyst must perform hypothesis testing tasks on sensitive data, but is able to leverage prior knowledge (public, but possibly erroneous or untrusted) about the data distribution. We design private algorithms in this augmented setting for three flagship distribution testing tasks, uniformity, identity, and closeness testing, whose sample complexity smoothly scales with the claimed quality of the auxiliary information. We complement our algorithms with information-theoretic lower bounds, showing that their sample complexity is optimal (up to logarithmic factors).

Problem

• Extend augmented distribution testing to differentially private setting.
• Design private algorithms for uniformity, identity, and closeness testing.
• Provide optimal sample complexity with information-theoretic lower bounds.

Innovation

• Extends augmented distribution testing framework
• Designs private algorithms for sensitive data
• Optimal sample complexity with auxiliary data