# Computationally tractable robust differentially private mean estimation

arXiv: https://arxiv.org/abs/2606.12654 · HTML: https://mlsanity.com/paper/2606.12654/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 40 references that are in the map.
- First posted on arXiv 10 Jun 2026.

## Builds on (most cited first, 22 of 22)

- [Concentrated Differential Privacy](https://mlsanity.com/paper/1603.01887/) (2016)
- [Privately Learning High-Dimensional Distributions](https://mlsanity.com/paper/1805.00216/) (2018)
- [CoinPress: Practical Private Mean and Covariance Estimation](https://mlsanity.com/paper/2006.06618/) (2020)
- [Private Mean Estimation of Heavy-Tailed Distributions](https://mlsanity.com/paper/2002.09464/) (2020)
- [Robust and Differentially Private Mean Estimation](https://mlsanity.com/paper/2102.09159/) (2021)
- [Differential privacy and robust statistics in high dimensions](https://mlsanity.com/paper/2111.06578/) (2021)
- [Private Hypothesis Selection](https://mlsanity.com/paper/1905.13229/) (2019)
- [Efficient Mean Estimation with Pure Differential Privacy via a Sum-of-Squares Exponential Mechanism](https://mlsanity.com/paper/2111.12981/) (2021)
- [Covariance-Aware Private Mean Estimation Without Private Covariance Estimation](https://mlsanity.com/paper/2106.13329/) (2021)
- [Private Robust Estimation by Stabilizing Convex Relaxations](https://mlsanity.com/paper/2112.03548/) (2021)
- [Instance-optimal Mean Estimation Under Differential Privacy](https://mlsanity.com/paper/2106.00463/) (2021)
- [Tight and Robust Private Mean Estimation with Few Users](https://mlsanity.com/paper/2110.11876/) (2021)
- [Fast, Sample-Efficient, Affine-Invariant Private Mean and Covariance Estimation for Subgaussian Distributions](https://mlsanity.com/paper/2301.12250/) (2023)
- [High-Dimensional Robust Mean Estimation via Gradient Descent](https://mlsanity.com/paper/2005.01378/) (2020)
- [A Fast Algorithm for Adaptive Private Mean Estimation](https://mlsanity.com/paper/2301.07078/) (2023)
- [Unbounded Differentially Private Quantile and Maximum Estimation](https://mlsanity.com/paper/2305.01177/) (2023)
- [Dimension-free Private Mean Estimation for Anisotropic Distributions](https://mlsanity.com/paper/2411.00775/) (2024)
- [Differentially private multivariate medians](https://mlsanity.com/paper/2210.06459/) (2022)
- [Differentially private projection-depth-based medians](https://mlsanity.com/paper/2312.07792/) (2023)
- [Differentially Private Boxplots](https://mlsanity.com/paper/2405.20415/) (2024)
- [Tukey Depth Mechanisms for Practical Private Mean Estimation](https://mlsanity.com/paper/2502.18698/) (2025)
- [Improved subsample-and-aggregate via the private modified winsorized mean](https://mlsanity.com/paper/2501.14095/) (2025)

## Abstract (arXiv)

We develop a new, differentially private mean estimator called the balloon mean. The main features of the balloon mean are that it is computationally tractable and enjoys robustness to outlying observations. It is based on an iterative clipping procedure over expanding Mahalanobis balls, or ``balloons.'' The method satisfies zero-concentrated differential privacy and depends on a small number of interpretable tuning parameters. We provide theoretical guarantees under heavy-tailed and contaminated elliptical models, characterizing its statistical performance and robustness to outliers. Extensive simulations demonstrate that the balloon mean is robust to heavy-tailed and contaminated data, and outperforms existing differentially private mean estimators in contaminated settings.