This paper studies how to approximate pufferfish privacy when the adversary's prior belief of the published data is Gaussian distributed. Using Monge's optimal transport plan, we show that $(\epsilon, \delta)$-pufferfish privacy is attained if the additive Laplace noise is calibrated to the differences in mean and variance of the Gaussian distributions conditioned on every discriminative secret pair. A typical application is the private release of the summation (or average) query, for which sufficient conditions are derived for approximating $\epsilon$-statistical indistinguishability in individual's sensitive data. The result is then extended to arbitrary prior beliefs trained by Gaussian mixture models (GMMs): calibrating Laplace noise to a convex combination of differences in mean and variance between Gaussian components attains $(\epsilon,\delta)$-pufferfish privacy.

翻译：本文研究当对手对发布数据的先验信念服从高斯分布时，如何近似河豚隐私。利用蒙日最优传输计划，我们证明：若将加性拉普拉斯噪声校准到基于每个可区分秘密对条件高斯的均值和方差差异，则能达到$(\epsilon,\delta)$-河豚隐私。一个典型应用是求和（或平均）查询的私有发布，为此推导了在个人敏感数据上近似$\epsilon$-统计不可区分性的充分条件。该结果进一步推广至由高斯混合模型训练的任意先验信念：将拉普拉斯噪声校准为高斯分量间均值和方差差异的凸组合，即可实现$(\epsilon,\delta)$-河豚隐私。