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

arXiv: https://arxiv.org/abs/2305.17148 · HTML: https://mlsanity.com/paper/2305.17148/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 61 references that are in the map.
- First posted on arXiv 26 May 2023.

## Builds on (most cited first, 22 of 22)

- [A Universal Law of Robustness via Isoperimetry](https://mlsanity.com/paper/2105.12806/) (2021)
- [Privately Learning High-Dimensional Distributions](https://mlsanity.com/paper/1805.00216/) (2018)
- [DP-MERF: Differentially Private Mean Embeddings with Random Features for Practical Privacy-Preserving Data Generation](https://mlsanity.com/paper/2002.11603/) (2020)
- [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)
- [A Dynamical System Perspective for Lipschitz Neural Networks](https://mlsanity.com/paper/2110.12690/) (2021)
- [The Noisy Power Method: A Meta Algorithm with Applications](https://mlsanity.com/paper/1311.2495/) (2013)
- [Geographic Spines in the 2020 Census Disclosure Avoidance System](https://mlsanity.com/paper/2203.16654/) (2022)
- [Private Synthetic Data for Multitask Learning and Marginal Queries](https://mlsanity.com/paper/2209.07400/) (2022)
- [Streaming PCA: Matching Matrix Bernstein and Near-Optimal Finite Sample Guarantees for Oja's Algorithm](https://mlsanity.com/paper/1602.06929/) (2016)
- [DP-PCA: Statistically Optimal and Differentially Private PCA](https://mlsanity.com/paper/2205.13709/) (2022)
- [Efficient Algorithms for Privately Releasing Marginals via Convex Relaxations](https://mlsanity.com/paper/1308.1385/) (2013)
- [Privately Learning Subspaces](https://mlsanity.com/paper/2106.00001/) (2021)
- [Differentially Private Covariance Revisited](https://mlsanity.com/paper/2205.14324/) (2022)
- [Differentially Private Neural Tangent Kernels for Privacy-Preserving Data Generation](https://mlsanity.com/paper/2303.01687/) (2023)
- [Differentially Private Database Release via Kernel Mean Embeddings](https://mlsanity.com/paper/1710.01641/) (2017)
- [Algorithmically Effective Differentially Private Synthetic Data](https://mlsanity.com/paper/2302.05552/) (2023)
- [Wishart Mechanism for Differentially Private Principal Components Analysis](https://mlsanity.com/paper/1511.05680/) (2015)
- [Private sampling: a noiseless approach for generating differentially private synthetic data](https://mlsanity.com/paper/2109.14839/) (2021)
- [Re-Analyze Gauss: Bounds for Private Matrix Approximation via Dyson Brownian Motion](https://mlsanity.com/paper/2211.06418/) (2022)
- [Covariance's Loss is Privacy's Gain: Computationally Efficient, Private and Accurate Synthetic Data](https://mlsanity.com/paper/2107.05824/) (2021)
- [Certified private data release for sparse Lipschitz functions](https://mlsanity.com/paper/2302.09680/) (2023)

## Built on by (most cited first, 4 of 4)

- [Online Differentially Private Synthetic Data Generation](https://mlsanity.com/paper/2402.08012/) (2024)
- [Private Continuous-Time Synthetic Trajectory Generation via Mean-Field Langevin Dynamics](https://mlsanity.com/paper/2506.12203/) (2025)
- [Minimax optimal differentially private synthetic data for smooth queries](https://mlsanity.com/paper/2602.01607/) (2026)
- [Geometry-Adaptive Mechanisms for Private Synthetic Data](https://mlsanity.com/paper/2609.33363/) (2026)

## 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.