# Differentially Private Algorithms for Learning Mixtures of Separated Gaussians

arXiv: https://arxiv.org/abs/1909.03951 · HTML: https://mlsanity.com/paper/1909.03951/

## Key facts

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

## Built on by (most cited first, 27 of 27)

- [Robust and Differentially Private Mean Estimation](https://mlsanity.com/paper/2102.09159/) (2021)
- [Efficient Mean Estimation with Pure Differential Privacy via a Sum-of-Squares Exponential Mechanism](https://mlsanity.com/paper/2111.12981/) (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)
- [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)
- [Differentially-Private Clustering of Easy Instances](https://mlsanity.com/paper/2112.14445/) (2021)
- [Private Distribution Learning with Public Data: The View from Sample Compression](https://mlsanity.com/paper/2308.06239/) (2023)
- [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 Normalizing Flows for Privacy-Preserving Density Estimation](https://mlsanity.com/paper/2103.14068/) (2021)
- [A Central Limit Theorem for Differentially Private Query Answering](https://mlsanity.com/paper/2103.08721/) (2021)
- [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)
- [A Simple and Practical Method for Reducing the Disparate Impact of Differential Privacy](https://mlsanity.com/paper/2312.11712/) (2023)
- [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)
- [High-Dimensional Differentially-Private EM Algorithm: Methods and Near-Optimal Statistical Guarantees](https://mlsanity.com/paper/2104.00245/) (2021)
- [Agnostic Private Density Estimation for GMMs via List Global Stability](https://mlsanity.com/paper/2407.04783/) (2024)
- [On Differentially Private U Statistics](https://mlsanity.com/paper/2407.04945/) (2024)
- [Improving the Utility of Differentially Private Clustering through Dynamical Processing](https://mlsanity.com/paper/2304.13886/) (2023)
- [Sample-Efficient Private Learning of Mixtures of Gaussians](https://mlsanity.com/paper/2411.02298/) (2024)
- [Subspace Recovery in Winsorized PCA: Insights into Accuracy and Robustness](https://mlsanity.com/paper/2502.16391/) (2025)

## Abstract (arXiv)

Learning the parameters of Gaussian mixture models is a fundamental and widely studied problem with numerous applications. In this work, we give new algorithms for learning the parameters of a high-dimensional, well separated, Gaussian mixture model subject to the strong constraint of differential privacy. In particular, we give a differentially private analogue of the algorithm of Achlioptas and McSherry. Our algorithm has two key properties not achieved by prior work: (1) The algorithm's sample complexity matches that of the corresponding non-private algorithm up to lower order terms in a wide range of parameters. (2) The algorithm does not require strong a priori bounds on the parameters of the mixture components.