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

arXiv: https://arxiv.org/abs/2410.09506 · HTML: https://mlsanity.com/paper/2410.09506/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 19 references that are in the map.
- First posted on arXiv 12 Oct 2024.

## Builds on (most cited first, 14 of 14)

- [Optimization Methods for Large-Scale Machine Learning](https://mlsanity.com/paper/1606.04838/) (2016)
- [Minimax Optimal Procedures for Locally Private Estimation](https://mlsanity.com/paper/1604.02390/) (2016)
- [Average-Case Averages: Private Algorithms for Smooth Sensitivity and Mean Estimation](https://mlsanity.com/paper/1906.02830/) (2019)
- [On Markov chain Monte Carlo methods for tall data](https://mlsanity.com/paper/1505.02827/) (2015)
- [Privacy Loss in Apple's Implementation of Differential Privacy on MacOS 10.12](https://mlsanity.com/paper/1709.02753/) (2017)
- [QLSD: Quantised Langevin stochastic dynamics for Bayesian federated learning](https://mlsanity.com/paper/2106.00797/) (2021)
- [Discrete Distribution Estimation under User-level Local Differential Privacy](https://mlsanity.com/paper/2211.03757/) (2022)
- [Local differential privacy: Elbow effect in optimal density estimation and adaptation over Besov ellipsoids](https://mlsanity.com/paper/1903.01927/) (2019)
- [Locally private non-asymptotic testing of discrete distributions is faster using interactive mechanisms](https://mlsanity.com/paper/2005.12601/) (2020)
- [A Huber Loss Minimization Approach to Mean Estimation under User-level Differential Privacy](https://mlsanity.com/paper/2405.13453/) (2024)
- [Towards Instance-Optimal Private Query Release](https://mlsanity.com/paper/1811.03763/) (2018)
- [The Role of Interactivity in Structured Estimation](https://mlsanity.com/paper/2203.06870/) (2022)
- [Rate Optimality and Phase Transition for User-Level Local Differential Privacy](https://mlsanity.com/paper/2405.11923/) (2024)
- [Linear Queries Estimation with Local Differential Privacy](https://mlsanity.com/paper/1810.02810/) (2018)

## Built on by (most cited first, 1 of 1)

- [Matrix Factorization for Practical Continual Mean Estimation Under User-Level Differential Privacy](https://mlsanity.com/paper/2601.22320/) (2026)

## Abstract (arXiv)

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.