Besides the Laplace distribution and the Gaussian distribution, there are
many more probability distributions which is not well-understood in terms of
privacy-preserving property of a random draw — one of which is the Dirichlet
distribution. In this work, we study the inherent privacy of releasing a single
draw 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 prove
accuracy guarantees of private Multinomial-Dirichlet sampling, which is
prevalent in Bayesian tasks, and private release of a normalized histogram. In
addition, with our results, it is possible to make Bayesian reinforcement
learning differentially private by modifying the Dirichlet sampling for state
transition probabilities.

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