# Private Mean Estimation with Person-Level Differential Privacy

arXiv: https://arxiv.org/abs/2405.20405 · HTML: https://mlsanity.com/paper/2405.20405/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2024.

## Built on by (most cited first, 6 of 6)

- [Differential Private Stochastic Optimization with Heavy-tailed Data: Towards Optimal Rates](https://mlsanity.com/paper/2408.09891/) (2024)
- [Optimal Differentially Private Sampling of Unbounded Gaussians](https://mlsanity.com/paper/2503.01766/) (2025)
- [High-Dimensional Differentially Private Quantile Regression: Distributed Estimation and Statistical Inference](https://mlsanity.com/paper/2508.05212/) (2025)
- [Privately Estimating Black-Box Statistics](https://mlsanity.com/paper/2510.00322/) (2025)
- [Black-Box Privacy Attacks on Shared Representations in Multitask Learning](https://mlsanity.com/paper/2506.16460/) (2025)
- [Matrix Factorization for Practical Continual Mean Estimation Under User-Level Differential Privacy](https://mlsanity.com/paper/2601.22320/) (2026)

## Abstract (arXiv)

We study person-level differentially private (DP) mean estimation in the case where each person holds multiple samples. DP here requires the usual notion of distributional stability when textitall of a person's datapoints can be modified. Informally, if n people each have m samples from an unknown d-dimensional distribution with bounded k-th moments, we show that [n = tilde Thetaleft(fracdα2 m + fracdα m1/2 varepsilon + fracdαk/(k-1) m varepsilon + fracdvarepsilonright)] people are necessary and sufficient to estimate the mean up to distance α in ℓ2-norm under varepsilon-differential privacy (and its common relaxations). In the multivariate setting, we give computationally efficient algorithms under approximate-DP and computationally inefficient algorithms under pure DP, and our nearly matching lower bounds hold for the most permissive case of approximate DP. Our computationally efficient estimators are based on the standard clip-and-noise framework, but the analysis for our setting requires both new algorithmic techniques and new analyses. In particular, our new bounds on the tails of sums of independent, vector-valued, bounded-moments random variables may be of interest.