Rényi Pufferfish Privacy with Gaussian-based Priors: From Single Gaussian to Mixture Model
For practitioners needing privacy guarantees on correlated data, this work provides less conservative mechanisms that improve utility, though it is an incremental extension of existing RPP frameworks.
The paper studies Gaussian mechanisms for Rényi Pufferfish Privacy (RPP) under Gaussian and Gaussian-mixture priors, deriving exact Rényi divergence and relaxed sufficient conditions. Experiments show an average noise reduction of 48.9% over a recent baseline, improving the privacy-utility trade-off for correlated data.
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.