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

Approximation of Pufferfish Privacy for Gaussian Priors