# Algorithmically Effective Differentially Private Synthetic Data

arXiv: https://arxiv.org/abs/2302.05552 · HTML: https://mlsanity.com/paper/2302.05552/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Feb 2023.

## Built on by (most cited first, 11 of 11)

- [Optimal Differentially Private Model Training with Public Data](https://mlsanity.com/paper/2306.15056/) (2023)
- [Differentially Private Low-dimensional Synthetic Data from High-dimensional Datasets](https://mlsanity.com/paper/2305.17148/) (2023)
- [Online Differentially Private Synthetic Data Generation](https://mlsanity.com/paper/2402.08012/) (2024)
- [Sharper Bounds for Chebyshev Moment Matching, with Applications](https://mlsanity.com/paper/2408.12385/) (2024)
- [Differentially Private Synthetic Data Generation for Relational Databases](https://mlsanity.com/paper/2405.18670/) (2024)
- [Private Evolution Converges](https://mlsanity.com/paper/2506.08312/) (2025)
- [Differentially Private Wasserstein Barycenters](https://mlsanity.com/paper/2510.03021/) (2025)
- [Private Synthetic Graph Generation and Fused Gromov-Wasserstein Distance](https://mlsanity.com/paper/2502.11778/) (2025)
- [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)

We present a highly effective algorithmic approach for generating varepsilon-differentially private synthetic data in a bounded metric space with near-optimal utility guarantees under the 1-Wasserstein distance. In particular, for a dataset X in the hypercube [0,1]d, our algorithm generates synthetic dataset Y such that the expected 1-Wasserstein distance between the empirical measure of X and Y is O((varepsilon n)-1/d) for d≥ 2, and is O(log2(varepsilon n)(varepsilon n)-1) for d=1. The accuracy guarantee is optimal up to a constant factor for d≥ 2, and up to a logarithmic factor for d=1. Our algorithm has a fast running time of O(varepsilon dn) for all d≥ 1 and demonstrates improved accuracy compared to the method in (Boedihardjo et al., 2022) for d≥ 2.