Distribution-Aware Mean Estimation under User-level Local Differential Privacy

TL;DR

This paper develops a distribution-aware mean estimation method under user-level local differential privacy, accounting for varying data sample sizes per user, and establishes bounds that match asymptotically.

Contribution

It introduces a novel mean estimation algorithm that considers the distribution of user data sizes and provides matching upper and lower bounds.

Findings

Achieves asymptotically tight risk bounds for mean estimation.

Extends previous work to scenarios with variable user data sizes.

Reduces to known bounds when all users have the same data size.

Abstract

We consider the problem of mean estimation under user-level local differential privacy, where $n$ users are contributing through their local pool of data samples. Previous work assume that the number of data samples is the same across users. In contrast, we consider a more general and realistic scenario where each user $u \in [n]$ owns $m_u$ data samples drawn from some generative distribution $\mu$; $m_u$ being unknown to the statistician but drawn from a known distribution $M$ over $\mathbb{N}^\star$. Based on a distribution-aware mean estimation algorithm, we establish an $M$-dependent upper bounds on the worst-case risk over $\mu$ for the task of mean estimation. We then derive a lower bound. The two bounds are asymptotically matching up to logarithmic factors and reduce to known bounds when $m_u = m$ for any user $u$.