# The Importance of Being Discrete: Measuring the Impact of Discretization in End-to-End Differentially Private Synthetic Data

arXiv: https://arxiv.org/abs/2504.06923 · HTML: https://mlsanity.com/paper/2504.06923/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 112 references that are in the map.
- First posted on arXiv 9 Apr 2025.

## Builds on (most cited first, 30 of 33)

- [Membership Inference Attacks against Machine Learning Models](https://mlsanity.com/paper/1610.05820/) (2016)
- [Differentially Private Generative Adversarial Network](https://mlsanity.com/paper/1802.06739/) (2018)
- [Hyperparameter Tuning with Renyi Differential Privacy](https://mlsanity.com/paper/2110.03620/) (2021)
- [Winning the NIST Contest: A scalable and general approach to differentially private synthetic data](https://mlsanity.com/paper/2108.04978/) (2021)
- [AIM: An Adaptive and Iterative Mechanism for Differentially Private Synthetic Data](https://mlsanity.com/paper/2201.12677/) (2022)
- [Benchmarking Differentially Private Synthetic Data Generation Algorithms](https://mlsanity.com/paper/2112.09238/) (2021)
- [Graphical-model based estimation and inference for differential privacy](https://mlsanity.com/paper/1901.09136/) (2019)
- [Iterative Methods for Private Synthetic Data: Unifying Framework and New Methods](https://mlsanity.com/paper/2106.07153/) (2021)
- [TAPAS: a Toolbox for Adversarial Privacy Auditing of Synthetic Data](https://mlsanity.com/paper/2211.06550/) (2022)
- [G-PATE: Scalable Differentially Private Data Generator via Private Aggregation of Teacher Discriminators](https://mlsanity.com/paper/1906.09338/) (2019)
- [Diffprivlib: The IBM Differential Privacy Library](https://mlsanity.com/paper/1907.02444/) (2019)
- [Differentially Private Query Release Through Adaptive Projection](https://mlsanity.com/paper/2103.06641/) (2021)
- [FIRST: A Framework for Optimizing Information Quality in Mobile Crowdsensing Systems](https://mlsanity.com/paper/1804.11147/) (2018)
- [New Oracle-Efficient Algorithms for Private Synthetic Data Release](https://mlsanity.com/paper/2007.05453/) (2020)
- [Differentially Private Mixture of Generative Neural Networks](https://mlsanity.com/paper/1709.04514/) (2017)
- [SoK: Privacy-Preserving Data Synthesis](https://mlsanity.com/paper/2307.02106/) (2023)
- [Private Synthetic Data for Multitask Learning and Marginal Queries](https://mlsanity.com/paper/2209.07400/) (2022)
- [Optimizing error of high-dimensional statistical queries under differential privacy](https://mlsanity.com/paper/1808.03537/) (2018)
- [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)
- [Kamino: Constraint-Aware Differentially Private Data Synthesis](https://mlsanity.com/paper/2012.15713/) (2020)
- [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)
- [Practical Differentially Private Hyperparameter Tuning with Subsampling](https://mlsanity.com/paper/2301.11989/) (2023)
- [Generating Private Synthetic Data with Genetic Algorithms](https://mlsanity.com/paper/2306.03257/) (2023)
- [Differentially Private Release of Israel's National Registry of Live Births](https://mlsanity.com/paper/2405.00267/) (2024)
- [Graphical vs. Deep Generative Models: Measuring the Impact of Differentially Private Mechanisms and Budgets on Utility](https://mlsanity.com/paper/2305.10994/) (2023)
- [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)

## Built on by (most cited first, 5 of 5)

- [dpmm: Differentially Private Marginal Models, a Library for Synthetic Tabular Data Generation](https://mlsanity.com/paper/2506.00322/) (2025)
- [Tight Auditing of Differential Privacy in MST and AIM](https://mlsanity.com/paper/2604.18352/) (2026)
- [Understanding the Impact of Data Domain Extraction on Synthetic Data Privacy](https://mlsanity.com/paper/2504.08254/) (2025)
- [Evaluating LLM Simulators as Differentially Private Data Generators](https://mlsanity.com/paper/2604.15461/) (2026)
- [Tight End-to-End Accounting for Differentially Private Synthetic Data](https://mlsanity.com/paper/2610.17249/) (2026)

## Abstract (arXiv)

Differentially Private (DP) generative marginal models are often used in the wild to release synthetic tabular datasets in lieu of sensitive data while providing formal privacy guarantees. These models approximate low-dimensional marginals or query workloads; crucially, they require the training data to be pre-discretized, i.e., continuous values need to first be partitioned into bins. However, as the range of values (or their domain) is often inferred directly from the training data, with the number of bins and bin edges typically defined arbitrarily, this approach can ultimately break end-to-end DP guarantees and may not always yield optimal utility. In this paper, we present an extensive measurement study of four discretization strategies in the context of DP marginal generative models. More precisely, we design DP versions of three discretizers (uniform, quantile, and k-means) and reimplement the PrivTree algorithm. We find that optimizing both the choice of discretizer and bin count can improve utility, on average, by almost 30% across six DP marginal models, compared to the default strategy and number of bins, with PrivTree being the best-performing discretizer in the majority of cases. We demonstrate that, while DP generative models with non-private discretization remain vulnerable to membership inference attacks, applying DP during discretization effectively mitigates this risk. Finally, we improve on an existing approach for automatically selecting the optimal number of bins, and achieve high utility while reducing both privacy budget consumption and computational overhead.