mlsanityData to 7 Oct 2026

Differentially Private Low-dimensional Synthetic Data from High-dimensional Datasets

arXiv 2305.17148 ↗First posted 26 May 2023cs.LG cs.CR cs.DScited by 4

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Abstract (arXiv)

Differentially private synthetic data provide a powerful mechanism to enable data analysis while protecting sensitive information about individuals. However, when the data lie in a high-dimensional space, the accuracy of the synthetic data suffers from the curse of dimensionality. In this paper, we propose a differentially private algorithm to generate low-dimensional synthetic data efficiently from a high-dimensional dataset with a utility guarantee with respect to the Wasserstein distance. A key step of our algorithm is a private principal component analysis (PCA) procedure with a near-optimal accuracy bound that circumvents the curse of dimensionality. Unlike the standard perturbation analysis, our analysis of private PCA works without assuming the spectral gap for the covariance matrix.

Key facts. Cited by 4 papers in the map (data through 7 Oct 2026). Builds on 22 of its 61 references that are in the map. First posted on arXiv 26 May 2023.

Builds on

22 of 61 references.

References · 22

  1. 2021A Universal Law of Robustness via Isoperimetrycited by 150
  2. 2018Privately Learning High-Dimensional Distributionscited by 103
  3. 2020DP-MERF: Differentially Private Mean Embeddings with Random Features for Practical Privacy-Preserving Data Generationcited by 78
  4. 2021Robust and Differentially Private Mean Estimationcited by 66
  5. 2021Differential privacy and robust statistics in high dimensionscited by 64
  6. 2021A Dynamical System Perspective for Lipschitz Neural Networkscited by 59
  7. 2013The Noisy Power Method: A Meta Algorithm with Applicationscited by 58
  8. 2022Geographic Spines in the 2020 Census Disclosure Avoidance Systemcited by 42
  9. 2022Private Synthetic Data for Multitask Learning and Marginal Queriescited by 35
  10. 2016Streaming PCA: Matching Matrix Bernstein and Near-Optimal Finite Sample Guarantees for Oja's Algorithmcited by 29
  11. 2022DP-PCA: Statistically Optimal and Differentially Private PCAcited by 24
  12. 2013Efficient Algorithms for Privately Releasing Marginals via Convex Relaxationscited by 17
10 more
  1. 2021Privately Learning Subspacescited by 16
  2. 2022Differentially Private Covariance Revisitedcited by 15
  3. 2023Differentially Private Neural Tangent Kernels for Privacy-Preserving Data Generationcited by 15
  4. 2017Differentially Private Database Release via Kernel Mean Embeddingscited by 12
  5. 2023Algorithmically Effective Differentially Private Synthetic Datacited by 11
  6. 2015Wishart Mechanism for Differentially Private Principal Components Analysiscited by 9
  7. 2021Private sampling: a noiseless approach for generating differentially private synthetic datacited by 8
  8. 2022Re-Analyze Gauss: Bounds for Private Matrix Approximation via Dyson Brownian Motioncited by 8
  9. 2021Covariance's Loss is Privacy's Gain: Computationally Efficient, Private and Accurate Synthetic Datacited by 7
  10. 2023Certified private data release for sparse Lipschitz functionscited by 7

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 1; 2026: 2.

4 papers.

  1. 2024Online Differentially Private Synthetic Data Generationcited by 4
  2. 2025Private Continuous-Time Synthetic Trajectory Generation via Mean-Field Langevin Dynamicscited by 0
  3. 2026Minimax optimal differentially private synthetic data for smooth queriescited by 0
  4. 2026Geometry-Adaptive Mechanisms for Private Synthetic Datacited by 0