Besides the Laplace distribution and the Gaussian distribution, there are many more probability distributions that are not well-understood in terms of privacy-preserving property -- 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 (the Dirichlet posterior sampling). As our main result, we provide a simple privacy guarantee of the Dirichlet posterior sampling with the framework of R\'enyi Differential Privacy (RDP). Consequently, the RDP guarantee allows us to derive a simpler form of the $(\varepsilon,\delta)$-differential privacy guarantee compared to those from the previous work. As an application, we use the RDP guarantee to derive a utility guarantee of the Dirichlet posterior sampling for privately releasing a normalized histogram, which is confirmed by our experimental results. Moreover, we demonstrate that the RDP guarantee can be used to track the privacy loss in Bayesian reinforcement learning.

翻译：除了Laplace分布和Gaussian分布之外,在隐私保护财产(其中之一是Drichlet分布)方面,还有更多的概率分布没有得到很好理解。在这项工作中,我们研究了从Drichlet 海报分布(Drichlet 海报分布抽样)中放出一幅图的固有隐私。我们的主要结果是,我们提供了一种简单的隐私保障,在R\'enyi 差异隐私(RDP)的框架内对Drichlet 后部取样进行。因此,RDP担保使我们能够获得比先前工作更简单的美元(varepsilon,\delta) 美元差异隐私保障形式。作为应用程序,我们利用RDP保证为Drichlet 海报的样本提供一种用于私人释放正常直方图的实用保障,我们实验结果证实了这一点。此外,我们证明RDP担保可以用来跟踪Bayesian强化学习的隐私损失。