# Differentially private sub-Gaussian location estimators

arXiv: https://arxiv.org/abs/1906.11923 · HTML: https://mlsanity.com/paper/1906.11923/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jun 2019.

## Built on by (most cited first, 9 of 9)

- [Differential privacy and robust statistics in high dimensions](https://mlsanity.com/paper/2111.06578/) (2021)
- [Efficient Mean Estimation with Pure Differential Privacy via a Sum-of-Squares Exponential Mechanism](https://mlsanity.com/paper/2111.12981/) (2021)
- [A Private and Computationally-Efficient Estimator for Unbounded Gaussians](https://mlsanity.com/paper/2111.04609/) (2021)
- [New Lower Bounds for Private Estimation and a Generalized Fingerprinting Lemma](https://mlsanity.com/paper/2205.08532/) (2022)
- [From Robustness to Privacy and Back](https://mlsanity.com/paper/2302.01855/) (2023)
- [A Polynomial Time, Pure Differentially Private Estimator for Binary Product Distributions](https://mlsanity.com/paper/2304.06787/) (2023)
- [Differentially private projection-depth-based medians](https://mlsanity.com/paper/2312.07792/) (2023)
- [Differentially private multivariate medians](https://mlsanity.com/paper/2210.06459/) (2022)
- [Improved subsample-and-aggregate via the private modified winsorized mean](https://mlsanity.com/paper/2501.14095/) (2025)

## Abstract (arXiv)

We tackle the problem of estimating a location parameter with differential privacy guarantees and sub-Gaussian deviations. Recent work in statistics has focused on the study of estimators that achieve sub-Gaussian type deviations even for heavy tailed data. We revisit some of these estimators through the lens of differential privacy and show that a naive application of the Laplace mechanism can lead to sub-optimal results. We design two private algorithms for estimating the median that lead to estimators with sub-Gaussian type errors. Unlike most existing differentially private median estimators, both algorithms are well defined for unbounded random variables that are not even required to have finite moments. We then turn to the problem of sub-Gaussian mean estimation and show that under heavy tails natural differentially private alternatives lead to strictly worse deviations than their non-private sub-Gaussian counterparts. This is in sharp contrast with recent results that show that from an asymptotic perspective the cost of differential privacy is negligible.