Rényi Differential Privacy Mechanisms for Posterior Sampling
This work addresses privacy concerns in Bayesian inference for domains like logistic regression, but it is incremental as it builds on existing RDP frameworks.
The paper tackles the problem of ensuring privacy when releasing samples from posterior distributions by leveraging Rényi Differential Privacy (RDP) and the mitigating effect of prior distributions, achieving arbitrary RDP guarantees with experimental validation.
Using a recently proposed privacy definition of Rényi Differential Privacy (RDP), 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.