# Understanding the Impact of Data Domain Extraction on Synthetic Data Privacy

arXiv: https://arxiv.org/abs/2504.08254 · HTML: https://mlsanity.com/paper/2504.08254/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Membership inference attacks, one of 12 directions in LLM safety and security.
- Builds on 14 of its 35 references that are in the map.
- First posted on arXiv 11 Apr 2025.

## Placed in

- LLM safety and security / [Membership inference attacks](https://mlsanity.com/safety/membership-inference-attacks/)

## Builds on (most cited first, 14 of 14)

- [Winning the NIST Contest: A scalable and general approach to differentially private synthetic data](https://mlsanity.com/paper/2108.04978/) (2021)
- [Graphical-model based estimation and inference for differential privacy](https://mlsanity.com/paper/1901.09136/) (2019)
- [Diffprivlib: The IBM Differential Privacy Library](https://mlsanity.com/paper/1907.02444/) (2019)
- [New Oracle-Efficient Algorithms for Private Synthetic Data Release](https://mlsanity.com/paper/2007.05453/) (2020)
- [SoK: Privacy-Preserving Data Synthesis](https://mlsanity.com/paper/2307.02106/) (2023)
- [Achilles' Heels: Vulnerable Record Identification in Synthetic Data Publishing](https://mlsanity.com/paper/2306.10308/) (2023)
- [Differentially Private k-Means Clustering](https://mlsanity.com/paper/1504.05998/) (2015)
- [PrivTree: A Differentially Private Algorithm for Hierarchical Decompositions](https://mlsanity.com/paper/1601.03229/) (2016)
- ["What do you want from theory alone?" Experimenting with Tight Auditing of Differentially Private Synthetic Data Generation](https://mlsanity.com/paper/2405.10994/) (2024)
- [Differentially Private Release of Israel's National Registry of Live Births](https://mlsanity.com/paper/2405.00267/) (2024)
- [The Elusive Pursuit of Reproducing PATE-GAN: Benchmarking, Auditing, Debugging](https://mlsanity.com/paper/2406.13985/) (2024)
- [dpart: Differentially Private Autoregressive Tabular, a General Framework for Synthetic Data Generation](https://mlsanity.com/paper/2207.05810/) (2022)
- [Synthetic Data: Methods, Use Cases, and Risks](https://mlsanity.com/paper/2303.01230/) (2023)
- [The Importance of Being Discrete: Measuring the Impact of Discretization in End-to-End Differentially Private Synthetic Data](https://mlsanity.com/paper/2504.06923/) (2025)

## Abstract (arXiv)

Privacy attacks, particularly membership inference attacks (MIAs), are widely used to assess the privacy of generative models for tabular synthetic data, including those with Differential Privacy (DP) guarantees. These attacks often exploit outliers, which are especially vulnerable due to their position at the boundaries of the data domain (e.g., at the minimum and maximum values). However, the role of data domain extraction in generative models and its impact on privacy attacks have been overlooked. In this paper, we examine three strategies for defining the data domain: assuming it is externally provided (ideally from public data), extracting it directly from the input data, and extracting it with DP mechanisms. While common in popular implementations and libraries, we show that the second approach breaks end-to-end DP guarantees and leaves models vulnerable. While using a provided domain (if representative) is preferable, extracting it with DP can also defend against popular MIAs, even at high privacy budgets.