On Choosing the $μ$ Parameter in Gaussian Differential Privacy

2026-06-08

AI Summary

This study addresses the challenge of appropriately calibrating the $\mu$ parameter in Gaussian Differential Privacy (GDP). By aligning the multiplicative advantage of a strong adversary’s membership inference attack under a fixed false positive rate, the precision at a fixed recall, and the standard privacy profile, the authors establish—for the first time—a principled, multi-dimensional mapping from pure differential privacy $\varepsilon$ to GDP $\mu$ grounded in attacker success rates. The work contributes a general conservative guideline $\mu \approx \varepsilon/5$, provides a lookup table for $\mu$ values across practical parameter regimes, and empirically validates the approximation’s effectiveness and conservativeness across diverse scenarios.

Abstract

Recent work argues for using Gaussian differential privacy (GDP) to report the privacy guarantees in privacy-preserving machine learning. We provide principled mappings from pure-DP $\varepsilon$ to GDP $μ$ by matching the worst-case success of a strong-adversary membership inference attack in terms of three metrics: multiplicative advantage at fixed FPR, precision at fixed recall, and the standard privacy profile. We tabulate $μ$ values across a useful range of parameters and recommend $μ\approx \varepsilon/5$ as a conservative general-purpose conversion.

Problem

• Gaussian differential privacy
• privacy parameter selection
• membership inference attack
• privacy-preserving machine learning
• differential privacy conversion

Innovation

• Gaussian Differential Privacy
• membership inference attack
• privacy parameter conversion
• pure differential privacy
• adversarial privacy analysis