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

TL;DR

This paper introduces a new matrix factorization approach for continual mean estimation that improves accuracy under user-level approximate differential privacy, addressing limitations of previous pure DP methods.

Contribution

It proposes a novel, efficient matrix factorization mechanism tailored for continual mean estimation under user-level approximate differential privacy, achieving lower error bounds.

Findings

Achieves asymptotically lower mean-squared error bounds.

Introduces a novel mean estimation specific matrix factorization.

Addresses limitations of pure differential privacy in continual estimation.

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.