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 $u$.

本研究解决了在用户级局部差分隐私下的均值估计问题，特别是在用户数据样本数量不一致的情况下。提出了一种分布感知的均值估计算法，并确定了该算法在最坏情况下的风险界限，结果在对数因素上渐近匹配，并在样本数量相同的情况下收敛到已知界限。这项工作为优化隐私保护下的均值估计提供了新的理论基础。

用户级局部差分隐私下的分布感知均值估计