Matrix Factorization for Practical Continual Mean Estimation Under User-Level Differential Privacy

2026-01-29

AI Summary

This work addresses the challenge of achieving high-accuracy mean estimation over continuously arriving data streams under user-level differential privacy constraints. We propose a novel matrix factorization mechanism based on approximate differential privacy, specifically designed for online mean estimation. By jointly optimizing the noise injection strategy and structured matrix decomposition, our approach provides strong privacy guarantees for each user’s entire data sequence while significantly reducing mean squared error. Compared to existing pure differential privacy mechanisms, our method circumvents their inherent lower bounds on noise magnitude, thereby achieving superior estimation accuracy and practical utility under user-level privacy protection.

Technology Category

• Machine Learning: Privacy
• Reasoning under Uncertainty: Stochastic Optimization
• Multiagent Systems: Mechanism Design

Application Category

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

Abstract

We study continual mean estimation, where data vectors arrive sequentially and the goal is to maintain accurate estimates of the running mean. We address this problem under user-level differential privacy, which protects each user's entire dataset even when they contribute multiple data points. Previous work on this problem has focused on pure differential privacy. While important, this approach limits applicability, as it leads to overly noisy estimates. In contrast, we analyze the problem under approximate differential privacy, adopting recent advances in the Matrix Factorization mechanism. We introduce a novel mean estimation specific factorization, which is both efficient and accurate, achieving asymptotically lower mean-squared error bounds in continual mean estimation under user-level differential privacy.

Problem

• continual mean estimation
• user-level differential privacy
• matrix factorization
• approximate differential privacy
• mean-squared error

Innovation

• user-level differential privacy
• continual mean estimation
• matrix factorization
• approximate differential privacy
• mean-squared error