R\'enyi Differential Privacy Mechanisms for Posterior Sampling

TL;DR

This paper explores the use of Renyi Differential Privacy (RDP) to analyze and improve privacy guarantees when releasing samples from posterior distributions, especially in exponential family models like logistic regression.

Contribution

It introduces new RDP mechanisms and provides a novel analysis for existing methods, leveraging prior distributions to enhance privacy in posterior sampling.

Findings

Proposed RDP mechanisms achieve arbitrary privacy guarantees.

Experimental results demonstrate effectiveness of the new methods.

Prior distributions help mitigate individual data influence.

Abstract

Using a recently proposed privacy definition of R\'enyi 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.