Differential Privacy of Dirichlet Posterior Sampling

Donlapark Ponnoprat

Keywords: differential privacy, Dirichlet distribution, Bayesian inference, Bayesian learning, posterior distribution

TL;DR: In this paper, we prove a simple privacy guarantee of the Dirichlet posterior sampling under the notion of truncated concentrated differential privacy (tCDP).

Abstract: We study the inherent privacy of releasing a single sample from a Dirichlet posterior distribution. As a complement to the previous study that provides general theories on the differential privacy of posterior sampling from exponential families, this study focuses specifically on the Dirichlet posterior sampling and its privacy guarantees. With the notion of truncated concentrated differential privacy (tCDP), we are able to derive a simple privacy guarantee of the Dirichlet posterior sampling, which effectively allows us to analyze its utility in various settings. Specifically, we provide accuracy guarantees of the Dirichlet posterior sampling in Multinomial-Dirichlet sampling and private normalized histogram publishing.

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