# FriendlyCore: Practical Differentially Private Aggregation

arXiv: https://arxiv.org/abs/2110.10132 · HTML: https://mlsanity.com/paper/2110.10132/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 44 references that are in the map.
- First posted on arXiv 19 Oct 2021.

## Builds on (most cited first, 15 of 15)

- [Concentrated Differential Privacy: Simplifications, Extensions, and Lower Bounds](https://mlsanity.com/paper/1605.02065/) (2016)
- [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)
- [Learning with User-Level Privacy](https://mlsanity.com/paper/2102.11845/) (2021)
- [Differentially Private Release and Learning of Threshold Functions](https://mlsanity.com/paper/1504.07553/) (2015)
- [Average-Case Averages: Private Algorithms for Smooth Sensitivity and Mean Estimation](https://mlsanity.com/paper/1906.02830/) (2019)
- [Instance-optimal Mean Estimation Under Differential Privacy](https://mlsanity.com/paper/2106.00463/) (2021)
- [Privately Learning Thresholds: Closing the Exponential Gap](https://mlsanity.com/paper/1911.10137/) (2019)
- [Differentially Private Algorithms for Learning Mixtures of Separated Gaussians](https://mlsanity.com/paper/1909.03951/) (2019)
- [Locating a Small Cluster Privately](https://mlsanity.com/paper/1604.05590/) (2016)
- [Differentially Private Confidence Intervals](https://mlsanity.com/paper/2001.02285/) (2020)
- [Privately Learning Subspaces](https://mlsanity.com/paper/2106.00001/) (2021)
- [Differentially Private Algorithms for Clustering with Stability Assumptions](https://mlsanity.com/paper/2106.12959/) (2021)

## Built on by (most cited first, 30 of 34)

- [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)
- [A Private and Computationally-Efficient Estimator for Unbounded Gaussians](https://mlsanity.com/paper/2111.04609/) (2021)
- [From Robustness to Privacy and Back](https://mlsanity.com/paper/2302.01855/) (2023)
- [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)
- [Private estimation algorithms for stochastic block models and mixture models](https://mlsanity.com/paper/2301.04822/) (2023)
- [Polynomial Time and Private Learning of Unbounded Gaussian Mixture Models](https://mlsanity.com/paper/2303.04288/) (2023)
- [Better and Simpler Lower Bounds for Differentially Private Statistical Estimation](https://mlsanity.com/paper/2310.06289/) (2023)
- [Private Distribution Learning with Public Data: The View from Sample Compression](https://mlsanity.com/paper/2308.06239/) (2023)
- [A Bias-Accuracy-Privacy Trilemma for Statistical Estimation](https://mlsanity.com/paper/2301.13334/) (2023)
- [User-level Differentially Private Stochastic Convex Optimization: Efficient Algorithms with Optimal Rates](https://mlsanity.com/paper/2311.03797/) (2023)
- [Lower Bounds for Private Estimation of Gaussian Covariance Matrices under All Reasonable Parameter Regimes](https://mlsanity.com/paper/2404.17714/) (2024)
- [Smooth Lower Bounds for Differentially Private Algorithms via Padding-and-Permuting Fingerprinting Codes](https://mlsanity.com/paper/2307.07604/) (2023)
- [Insufficient Statistics Perturbation: Stable Estimators for Private Least Squares](https://mlsanity.com/paper/2404.15409/) (2024)
- [Dimension-free Private Mean Estimation for Anisotropic Distributions](https://mlsanity.com/paper/2411.00775/) (2024)
- [A Polynomial Time, Pure Differentially Private Estimator for Binary Product Distributions](https://mlsanity.com/paper/2304.06787/) (2023)
- [Mixtures of Gaussians are Privately Learnable with a Polynomial Number of Samples](https://mlsanity.com/paper/2309.03847/) (2023)
- [Faster Algorithms for User-Level Private Stochastic Convex Optimization](https://mlsanity.com/paper/2410.18391/) (2024)
- [Urania: Differentially Private Insights into AI Use](https://mlsanity.com/paper/2506.04681/) (2025)
- [Sample-Optimal Locally Private Hypothesis Selection and the Provable Benefits of Interactivity](https://mlsanity.com/paper/2312.05645/) (2023)
- [Not All Learnable Distribution Classes are Privately Learnable](https://mlsanity.com/paper/2402.00267/) (2024)
- [Private Geometric Median](https://mlsanity.com/paper/2406.07407/) (2024)
- [Tukey Depth Mechanisms for Practical Private Mean Estimation](https://mlsanity.com/paper/2502.18698/) (2025)
- [The Relative Gaussian Mechanism and its Application to Private Gradient Descent](https://mlsanity.com/paper/2308.15250/) (2023)
- [On Differentially Private Subspace Estimation in a Distribution-Free Setting](https://mlsanity.com/paper/2402.06465/) (2024)
- [Improved subsample-and-aggregate via the private modified winsorized mean](https://mlsanity.com/paper/2501.14095/) (2025)
- [Private Geometric Median in Nearly-Linear Time](https://mlsanity.com/paper/2505.20189/) (2025)
- [Privately Estimating Black-Box Statistics](https://mlsanity.com/paper/2510.00322/) (2025)
- [On the Curse of Dimensionality in Private Sparse Covariance Estimation and PCA](https://mlsanity.com/paper/2606.21951/) (2026)

## Abstract (arXiv)

Differentially private algorithms for common metric aggregation tasks, such as clustering or averaging, often have limited practicality due to their complexity or to the large number of data points that is required for accurate results. We propose a simple and practical tool, mathsfFriendlyCore, that takes a set of points cal D from an unrestricted (pseudo) metric space as input. When cal D has effective diameter r, mathsfFriendlyCore returns a "stable" subset cal C subseteq cal D that includes all points, except possibly few outliers, and is em certified to have diameter r. mathsfFriendlyCore can be used to preprocess the input before privately aggregating it, potentially simplifying the aggregation or boosting its accuracy. Surprisingly, mathsfFriendlyCore is light-weight with no dependence on the dimension. We empirically demonstrate its advantages in boosting the accuracy of mean estimation and clustering tasks such as k-means and k-GMM, outperforming tailored methods.