With the newly proposed privacy definition of Rényi Differential Privacy (RDP) in (Mironov, 2017), we re-examine the inherent privacy of releasing a single sample from a posterior distribution. We exploit the impact of the prior distribution in mitigating the influence of individual data points. In particular, we focus on sampling from an exponential family and specific generalized linear models, such as logistic regression. We propose novel RDP mechanisms as well as offering a new RDP analysis for an existing method in order to add value to the RDP framework. Each method is capable of achieving arbitrary RDP privacy guarantees, and we offer experimental results of their efficacy.

This paper analyzes the privacy cost of posterior sampling for exponential family posteriors and generalized linear models by using the recently proposed privacy definition of Renyi-DP. Specifically, they applied the privacy analyses to two domains and presented experimental results for Beta-Bernoulli sampling and Bayesian Logistic Regression. In my opinion, the privacy analyses that the paper considers can be interesting and valuable for the community. But, the paper does not motivate enough the necessity of the usage of Renyi-DP. It is a relaxed notion of pure DP like CDP and z-CDP but the readers cannot learn from the paper that when they can use it or why should they use it.

With the newly proposed privacy definition of Rényi Differential Privacy (RDP) in (Mironov, 2017), we re-examine the inherent privacy of releasing a single sample from a posterior distribution. We exploit the impact of the prior distribution in mitigating the influence of individual data points. In particular, we focus on sampling from an exponential family and specific generalized linear models, such as logistic regression. We propose novel RDP mechanisms as well as offering a new RDP analysis for an existing method in order to add value to the RDP framework. Each method is capable of achieving arbitrary RDP privacy guarantees, and we offer experimental results of their efficacy.