# CoinPress: Practical Private Mean and Covariance Estimation

arXiv: https://arxiv.org/abs/2006.06618 · HTML: https://mlsanity.com/paper/2006.06618/

## Key facts

- Cited by 74 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2020.

## Built on by (most cited first, 30 of 74)

- [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)
- [Efficient Mean Estimation with Pure Differential Privacy via a Sum-of-Squares Exponential Mechanism](https://mlsanity.com/paper/2111.12981/) (2021)
- [Public Data-Assisted Mirror Descent for Private Model Training](https://mlsanity.com/paper/2112.00193/) (2021)
- [Covariance-Aware Private Mean Estimation Without Private Covariance Estimation](https://mlsanity.com/paper/2106.13329/) (2021)
- [Private and polynomial time algorithms for learning Gaussians and beyond](https://mlsanity.com/paper/2111.11320/) (2021)
- [Private Robust Estimation by Stabilizing Convex Relaxations](https://mlsanity.com/paper/2112.03548/) (2021)
- [FriendlyCore: Practical Differentially Private Aggregation](https://mlsanity.com/paper/2110.10132/) (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)
- [Private Estimation with Public Data](https://mlsanity.com/paper/2208.07984/) (2022)
- [DP-PCA: Statistically Optimal and Differentially Private PCA](https://mlsanity.com/paper/2205.13709/) (2022)
- [Polynomial Time and Private Learning of Unbounded Gaussian Mixture Models](https://mlsanity.com/paper/2303.04288/) (2023)
- [Differentially-Private Clustering of Easy Instances](https://mlsanity.com/paper/2112.14445/) (2021)
- [Differential Privacy Over Riemannian Manifolds](https://mlsanity.com/paper/2111.02516/) (2021)
- [Choosing Public Datasets for Private Machine Learning via Gradient Subspace Distance](https://mlsanity.com/paper/2303.01256/) (2023)
- [Differentially Private Covariance Revisited](https://mlsanity.com/paper/2205.14324/) (2022)
- [Privately Learning Mixtures of Axis-Aligned Gaussians](https://mlsanity.com/paper/2106.02162/) (2021)
- [Private High-Dimensional Hypothesis Testing](https://mlsanity.com/paper/2203.01537/) (2022)
- [Differentially private Riemannian optimization](https://mlsanity.com/paper/2205.09494/) (2022)
- [A Bias-Accuracy-Privacy Trilemma for Statistical Estimation](https://mlsanity.com/paper/2301.13334/) (2023)
- [A Fast Algorithm for Adaptive Private Mean Estimation](https://mlsanity.com/paper/2301.07078/) (2023)
- [Differentially Private Regression with Unbounded Covariates](https://mlsanity.com/paper/2202.11199/) (2022)
- [Differentially Private Bootstrap: New Privacy Analysis and Inference Strategies](https://mlsanity.com/paper/2210.06140/) (2022)
- [Non-parametric Differentially Private Confidence Intervals for the Median](https://mlsanity.com/paper/2106.10333/) (2021)
- [Insufficient Statistics Perturbation: Stable Estimators for Private Least Squares](https://mlsanity.com/paper/2404.15409/) (2024)
- [Towards hyperparameter-free optimization with differential privacy](https://mlsanity.com/paper/2503.00703/) (2025)
- [(Nearly) Optimal Private Linear Regression via Adaptive Clipping](https://mlsanity.com/paper/2207.04686/) (2022)
- [Shape And Structure Preserving Differential Privacy](https://mlsanity.com/paper/2209.12667/) (2022)
- [On the Statistical Complexity of Estimation and Testing under Privacy Constraints](https://mlsanity.com/paper/2210.02215/) (2022)

## Abstract (arXiv)

We present simple differentially private estimators for the mean and covariance of multivariate sub-Gaussian data that are accurate at small sample sizes. We demonstrate the effectiveness of our algorithms both theoretically and empirically using synthetic and real-world datasets -- showing that their asymptotic error rates match the state-of-the-art theoretical bounds, and that they concretely outperform all previous methods. Specifically, previous estimators either have weak empirical accuracy at small sample sizes, perform poorly for multivariate data, or require the user to provide strong a priori estimates for the parameters.