# Improved subsample-and-aggregate via the private modified winsorized mean

arXiv: https://arxiv.org/abs/2501.14095 · HTML: https://mlsanity.com/paper/2501.14095/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 36 references that are in the map.
- First posted on arXiv 23 Jan 2025.

## Builds on (most cited first, 23 of 23)

- [Semi-supervised Knowledge Transfer for Deep Learning from Private Training Data](https://mlsanity.com/paper/1610.05755/) (2016)
- [Mean estimation and regression under heavy-tailed distributions--a survey](https://mlsanity.com/paper/1906.04280/) (2019)
- [Finite Sample Differentially Private Confidence Intervals](https://mlsanity.com/paper/1711.03908/) (2017)
- [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)
- [Average-Case Averages: Private Algorithms for Smooth Sensitivity and Mean Estimation](https://mlsanity.com/paper/1906.02830/) (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)
- [FriendlyCore: Practical Differentially Private Aggregation](https://mlsanity.com/paper/2110.10132/) (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)
- [Easy Differentially Private Linear Regression](https://mlsanity.com/paper/2208.07353/) (2022)
- [A Fast Algorithm for Adaptive Private Mean Estimation](https://mlsanity.com/paper/2301.07078/) (2023)
- [Differentially private sub-Gaussian location estimators](https://mlsanity.com/paper/1906.11923/) (2019)
- [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 projection-depth-based medians](https://mlsanity.com/paper/2312.07792/) (2023)
- [Model-Agnostic Private Learning via Stability](https://mlsanity.com/paper/1803.05101/) (2018)
- [Differentially Private Boxplots](https://mlsanity.com/paper/2405.20415/) (2024)

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

- [Computationally tractable robust differentially private mean estimation](https://mlsanity.com/paper/2606.12654/) (2026)

## Abstract (arXiv)

We develop a univariate, differentially private mean estimator, called the private modified winsorized mean, designed to be used as the aggregator in subsample-and-aggregate. We demonstrate, via real data analysis, that common differentially private multivariate mean estimators may not perform well as the aggregator, even in large datasets, motivating our developments.We show that the modified winsorized mean is minimax optimal for several, large classes of distributions, even under adversarial contamination. We also demonstrate that, empirically, the private modified winsorized mean performs well compared to other private mean estimates. We consider the modified winsorized mean as the aggregator in subsample-and-aggregate, deriving a finite sample deviations bound for a subsample-and-aggregate estimate generated with the new aggregator. This result yields two important insights: (i) the optimal choice of subsamples depends on the bias of the estimator computed on the subsamples, and (ii) the rate of convergence of the subsample-and-aggregate estimator depends on the robustness of the estimator computed on the subsamples.