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

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 ∈ [n] owns mu data samples drawn from some generative distribution μ; mu being unknown to the statistician but drawn from a known distribution M over mathbbN^star. Based on a distribution-aware mean estimation algorithm, we establish an M-dependent upper bounds on the worst-case risk over μ 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 mu = m for any user u.