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

TL;DR

The paper tackles how discretization affects end-to-end differential privacy in synthetic tabular data, highlighting that the discretization step can dominate privacy-utility tradeoffs. It introduces DP adaptations of four discretizers (uniform, quantile, k-means, PrivTree) and reimplements PrivTree within a DP pipeline, coupled with five DP marginal models and a DP baseline. Through an extensive measurement study on controlled and real datasets across multiple privacy budgets, it shows that optimizing both the discretizer and the bin count yields substantial utility gains (around 30% on average), with PrivTree often providing the best performance and DL-bin optimization (RL-OPT) delivering up to a 41% improvement over naive baselines. It also demonstrates that applying DP to domain extraction reduces membership inference risk, albeit with a modest utility cost, underscoring the need for end-to-end DP discipline in discretization and pre-processing for trustworthy synthetic data releases.

Abstract

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.

Figures (19)

• Figure 1: Utility of four DP discretizers, averaged across six DP generative models ($\epsilon=1$) and three datasets (US3).
• Figure 2: Utility of default discretizer ( uniform, 20 bins) and optimal discretizer/bin count for six DP generative models ($\epsilon=1$), averaged across three datasets (US3).
• Figure 3: The four experimental settings (three focused on utility and one on privacy) used in our measurement study.
• Figure 4: Six controlled distributions and their discretization by four DP discretizers with 10 bins and $\epsilon=\infty$.
• Figure 5: Utility of DP discretizers, averaged across five controlled distributions (US1).