# Privacy of synthetic data: a statistical framework

arXiv: https://arxiv.org/abs/2109.01748 · HTML: https://mlsanity.com/paper/2109.01748/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Sep 2021.

## Built on by (most cited first, 10 of 10)

- [Post-processing Private Synthetic Data for Improving Utility on Selected Measures](https://mlsanity.com/paper/2305.15538/) (2023)
- [Leveraging Generative AI for Urban Digital Twins: A Scoping Review on the Autonomous Generation of Urban Data, Scenarios, Designs, and 3D City Models for Smart City Advancement](https://mlsanity.com/paper/2405.19464/) (2024)
- [Differentially Private Synthetic Data with Private Density Estimation](https://mlsanity.com/paper/2405.04554/) (2024)
- [Differentially Private Synthetic Data Generation for Relational Databases](https://mlsanity.com/paper/2405.18670/) (2024)
- [Privacy without Noisy Gradients: Slicing Mechanism for Generative Model Training](https://mlsanity.com/paper/2410.19941/) (2024)
- [Privacy Risks and Preservation Methods in Explainable Artificial Intelligence: A Scoping Review](https://mlsanity.com/paper/2505.02828/) (2025)
- [Methods for generating and evaluating synthetic longitudinal patient data: a systematic review](https://mlsanity.com/paper/2309.12380/) (2023)
- [Optimizing Mouse Dynamics for User Authentication by Machine Learning: Addressing Data Sufficiency, Accuracy-Practicality Trade-off, and Model Performance Challenges](https://mlsanity.com/paper/2504.21415/) (2025)
- [Fixed-Parameter Tractability of Private Synthetic Data Generation](https://mlsanity.com/paper/2606.11283/) (2026)
- [Geometry-Adaptive Mechanisms for Private Synthetic Data](https://mlsanity.com/paper/2609.33363/) (2026)

## Abstract (arXiv)

Privacy-preserving data analysis is emerging as a challenging problem with far-reaching impact. In particular, synthetic data are a promising concept toward solving the aporetic conflict between data privacy and data sharing. Yet, it is known that accurately generating private, synthetic data of certain kinds is NP-hard. We develop a statistical framework for differentially private synthetic data, which enables us to circumvent the computational hardness of the problem. We consider the true data as a random sample drawn from a population Omega according to some unknown density. We then replace Omega by a much smaller random subset Omega^*, which we sample according to some known density. We generate synthetic data on the reduced space Omega^* by fitting the specified linear statistics obtained from the true data. To ensure privacy we use the common Laplacian mechanism. Employing the concept of Renyi condition number, which measures how well the sampling distribution is correlated with the population distribution, we derive explicit bounds on the privacy and accuracy provided by the proposed method.