# Private sampling: a noiseless approach for generating differentially private synthetic data

arXiv: https://arxiv.org/abs/2109.14839 · HTML: https://mlsanity.com/paper/2109.14839/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Sep 2021.

## Built on by (most cited first, 8 of 8)

- [Differentially Private Low-dimensional Synthetic Data from High-dimensional Datasets](https://mlsanity.com/paper/2305.17148/) (2023)
- [A Simple and Practical Method for Reducing the Disparate Impact of Differential Privacy](https://mlsanity.com/paper/2312.11712/) (2023)
- [Online Differentially Private Synthetic Data Generation](https://mlsanity.com/paper/2402.08012/) (2024)
- [Differentially Private Synthetic Data with Private Density Estimation](https://mlsanity.com/paper/2405.04554/) (2024)
- [Privacy without Noisy Gradients: Slicing Mechanism for Generative Model Training](https://mlsanity.com/paper/2410.19941/) (2024)
- [Tunable correlation retention: A statistical method for generating synthetic data](https://mlsanity.com/paper/2403.01471/) (2024)
- [Reveal-or-Obscure: A Differentially Private Sampling Algorithm for Discrete Distributions](https://mlsanity.com/paper/2504.14696/) (2025)
- [Geometry-Adaptive Mechanisms for Private Synthetic Data](https://mlsanity.com/paper/2609.33363/) (2026)

## Abstract (arXiv)

In a world where artificial intelligence and data science become omnipresent, data sharing is increasingly locking horns with data-privacy concerns. Differential privacy has emerged as a rigorous framework for protecting individual privacy in a statistical database, while releasing useful statistical information about the database. The standard way to implement differential privacy is to inject a sufficient amount of noise into the data. However, in addition to other limitations of differential privacy, this process of adding noise will affect data accuracy and utility. Another approach to enable privacy in data sharing is based on the concept of synthetic data. The goal of synthetic data is to create an as-realistic-as-possible dataset, one that not only maintains the nuances of the original data, but does so without risk of exposing sensitive information. The combination of differential privacy with synthetic data has been suggested as a best-of-both-worlds solutions. In this work, we propose the first noisefree method to construct differentially private synthetic data; we do this through a mechanism called "private sampling". Using the Boolean cube as benchmark data model, we derive explicit bounds on accuracy and privacy of the constructed synthetic data. The key mathematical tools are hypercontractivity, duality, and empirical processes. A core ingredient of our private sampling mechanism is a rigorous "marginal correction" method, which has the remarkable property that importance reweighting can be utilized to exactly match the marginals of the sample to the marginals of the population.