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.
翻译:除了Laplace分布和Gaussian分布之外,在随机抽取(其中之一是Drichlet分布)的隐私保护属性方面,还有更多的概率分布,这些分布在随机抽取(其中之一是Drichlet分布)的隐私保护方面没有很好地理解。在这项工作中,我们研究了从Drichlet 海报分布中释放单一抽取的固有隐私。作为对前一份研究报告的补充,该研究报告提供了关于指数式家庭后方取样的隐私差异的一般性理论,本研究报告特别侧重于Drichlet 后方取样及其隐私保障。有了疏漏集中的隐私(tCDP)的概念,我们能够获得Drichlet 后方取样的简单隐私保障,从而使我们能够有效地分析其在不同环境中的实用性。具体地说,我们证明了私人多营养-Drichlet取样的准确性保障,这在Bayesian的任务中十分普遍,以及私人发布一种标准化的直方图。此外,我们的结果是,通过修改Drichlet取样以改变国家过渡性稳定性,使Bayesian的强化学习有差异。