Rényi Pufferfish Privacy with Gaussian-based Priors: From Single Gaussian to Mixture Model

2026-04-26

AI Summary

This work addresses the excessive conservatism of existing Rényi Pufferfish privacy mechanisms when handling correlated data, which leads to significant utility loss. To overcome this limitation, the authors propose noise-adding mechanisms based on Gaussian and Gaussian mixture priors. They derive, for the first time, the exact Rényi divergence under Gaussian perturbation with a single Gaussian prior, providing a closed-form sufficient condition, and extend this analysis to multimodal, non-Gaussian settings. By integrating the Gaussian mechanism, Rényi divergence analysis, optimal transport theory, and Gaussian mixture approximation techniques, the proposed approach reduces the required noise magnitude by 48.9% on average across three UCI datasets, substantially improving data utility while maintaining rigorous privacy guarantees.

Technology Category

• Machine Learning: Privacy
• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Security and Privacy: Data transparency and provenance
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

Rényi Pufferfish Privacy (RPP) provides a Rényi divergence-based privacy framework for correlated data, but existing $\infty$-Wasserstein mechanisms are often conservative and sacrifice data utility. We study Gaussian mechanisms for RPP under Gaussian and Gaussian-mixture priors. For single Gaussian priors, we derive the exact Rényi divergence after Gaussian perturbation, obtain a relaxed closed-form sufficient condition for $(α,ε)$-RPP, and characterize the monotonicity of the calibrated noise with respect to the privacy budget $ε$ and the Rényi order $α$. To handle more general non-Gaussian and multimodal priors, we approximate secret-conditioned outputs with Gaussian mixture models and introduce an optimal-transport-based sufficient condition for RPP. Experiments on three UCI datasets with statistical (\textsc{RAW}, \textsc{MEAN}) and model-output (\textsc{BNN}, \textsc{GP}) queries show that our prior-aware mechanisms consistently require less noise than a recent RPP additive-noise baseline, achieving an average noise reduction of 48.9\%. These results show that our mechanisms can substantially improve the privacy-utility trade-off under RPP.

Problem

• Rényi Pufferfish Privacy
• Gaussian mechanisms
• privacy-utility trade-off
• correlated data
• additive noise

Innovation

• Rényi Pufferfish Privacy
• Gaussian Mechanism
• Gaussian Mixture Model
• Optimal Transport
• Privacy-Utility Trade-off