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.

翻译：Rényi Pufferfish隐私（RPP）为关联数据提供了一种基于Rényi散度的隐私框架，但现有的∞-Wasserstein机制通常较为保守且牺牲数据效用。我们研究了高斯机制在单高斯和高斯混合先验下的RPP表现。针对单高斯先验，我们推导了高斯扰动后的精确Rényi散度，获得了满足(α,ε)-RPP的松弛闭式充分条件，并刻画了校准噪声随隐私预算ε和Rényi阶数α的单调性。为处理更一般的非高斯和多峰先验，我们采用高斯混合模型近似秘密条件输出，并引入基于最优传输的RPP充分条件。在三个UCI数据集上针对统计型（\textsc{RAW}、\textsc{MEAN}）和模型输出型（\textsc{BNN}、\textsc{GP}）查询的实验表明，本文提出的先验感知机制始终比近期RPP加性噪声基线方法所需噪声更少，平均噪声降低48.9%。这些结果证明了我们的机制能够显著改善RPP下的隐私-效用权衡。