Approximation of Pufferfish Privacy for Gaussian Priors

• URL: http://arxiv.org/abs/2401.12391v2
• Date: Mon, 6 May 2024 22:07:29 GMT
• Title: Approximation of Pufferfish Privacy for Gaussian Priors
• Authors: Ni Ding,
• Abstract summary: 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.
• Score: 6.2584995033090625
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: 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.

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