Bounding User Contributions for User-Level Differentially Private Mean Estimation

TL;DR

This paper characterizes the optimal data preprocessing strategy for user-level differentially private mean estimation, achieving minimal worst-case error even with heterogeneous data, and demonstrates improved average-case performance over existing methods.

Contribution

It provides a precise, distribution-independent characterization of the optimal clipping strategy for private mean estimation with heterogeneous data.

Findings

Optimal preprocessing minimizes worst-case error.

Proposed strategy outperforms existing methods in average-case error.

Effective under data heterogeneity and real-world conditions.

Abstract

We revisit the problem of releasing the sample mean of bounded samples in a dataset, privately, under user-level $\varepsilon$-differential privacy (DP). We aim to derive the optimal method of preprocessing data samples, within a canonical class of processing strategies, in terms of the error in estimation. Typical error analyses of such \emph{bounding} (or \emph{clipping}) strategies in the literature assume that the data samples are independent and identically distributed (i.i.d.), and sometimes also that all users contribute the same number of samples (data homogeneity) -- assumptions that do not accurately model real-world data distributions. Our main result in this work is a precise characterization of the preprocessing strategy that gives rise to the smallest \emph{worst-case} error over all datasets -- a \emph{distribution-independent} error metric -- while allowing for data heterogeneity. We also show via experimental studies that even for i.i.d. real-valued samples, our clipping strategy performs much better, in terms of \emph{average-case} error, than the widely used bounding strategy of Amin et al. (2019).