Tight Auditing of Differential Privacy in MST and AIM

Abstract

State-of-the-art Differentially Private (DP) synthetic data generators such as MST and AIM are widely used, yet tightly auditing their privacy guarantees remains challenging. We introduce a Gaussian Differential Privacy (GDP)-based auditing framework that measures privacy via the full false-positive/false-negative tradeoff. Applied to MST and AIM under worst-case settings, our method provides the first tight audits in the strong-privacy regime. For $(\epsilon ,\delta )=(1,10^{-2})$, we obtain ${\mu }_{emp}\approx 0.43$ vs. implied $\mu =0.45$, showing a small theory-practice gap. Our code is publicly available: https://github.com/sassoftware/dpmm.

Accepted to the Theory and Practice of Differential Privacy Workshop (TPDP 2026)