mlsanityData to 14 Oct 2026

Differentially Private Algorithms for Learning Mixtures of Separated Gaussians

arXiv 1909.03951 ↗First posted 9 Sep 2019cs.DS cs.CR cs.ITcited by 27

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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.

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

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Citing papers per year: 2021: 11; 2022: 3; 2023: 8; 2024: 4; 2025: 1.

27 papers.

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  1. 2021Robust and Differentially Private Mean Estimationcited by 66
  2. 2021Efficient Mean Estimation with Pure Differential Privacy via a Sum-of-Squares Exponential Mechanismcited by 50
  3. 2021Private and polynomial time algorithms for learning Gaussians and beyondcited by 39
  4. 2021Private Robust Estimation by Stabilizing Convex Relaxationscited by 38
  5. 2021FriendlyCore: Practical Differentially Private Aggregationcited by 34
  6. 2021A Private and Computationally-Efficient Estimator for Unbounded Gaussianscited by 34
  7. 2022New Lower Bounds for Private Estimation and a Generalized Fingerprinting Lemmacited by 33
  8. 2022Private Estimation with Public Datacited by 32
  9. 2023Private estimation algorithms for stochastic block models and mixture modelscited by 21
  10. 2023Polynomial Time and Private Learning of Unbounded Gaussian Mixture Modelscited by 19
  11. 2021Differentially-Private Clustering of Easy Instancescited by 17
  12. 2023Private Distribution Learning with Public Data: The View from Sample Compressioncited by 14
15 more
  1. 2021Privately Learning Mixtures of Axis-Aligned Gaussianscited by 13
  2. 2022Private High-Dimensional Hypothesis Testingcited by 12
  3. 2021Differentially Private Normalizing Flows for Privacy-Preserving Density Estimationcited by 10
  4. 2021A Central Limit Theorem for Differentially Private Query Answeringcited by 7
  5. 2023A Polynomial Time, Pure Differentially Private Estimator for Binary Product Distributionscited by 5
  6. 2023Mixtures of Gaussians are Privately Learnable with a Polynomial Number of Samplescited by 5
  7. 2023A Simple and Practical Method for Reducing the Disparate Impact of Differential Privacycited by 4
  8. 2023Sample-Optimal Locally Private Hypothesis Selection and the Provable Benefits of Interactivitycited by 3
  9. 2024Not All Learnable Distribution Classes are Privately Learnablecited by 3
  10. 2021High-Dimensional Differentially-Private EM Algorithm: Methods and Near-Optimal Statistical Guaranteescited by 2
  11. 2024Agnostic Private Density Estimation for GMMs via List Global Stabilitycited by 2
  12. 2024On Differentially Private U Statisticscited by 2
  13. 2023Improving the Utility of Differentially Private Clustering through Dynamical Processingcited by 0
  14. 2024Sample-Efficient Private Learning of Mixtures of Gaussianscited by 0
  15. 2025Subspace Recovery in Winsorized PCA: Insights into Accuracy and Robustnesscited by 0