Differential Privacy in a Bayesian setting through posterior sampling
Christos Dimitrakakis, Blaine A. Nelson, Zhang, Zuhe, Aikaterini Mitrokotsa, Benjamin I. P. Rubinstein · arXiv (Cornell University) · 2013
We examine the robustness and privacy properties of Bayesian inference, under assumptions on the prior. With no modifications to the Bayesian framework, we show that a simple posterior sampling algorithm results in uniform utility and privacy guarantees. In more detail, we generalise the concept of differential privacy to arbitrary dataset distances, outcome spaces and distribution families. We then prove bounds on the robustness of the posterior, introduce a posterior sampling mechanism, show that it is differentially private and provide finite sample bounds for distinguishability-based privacy under a strong adversarial model. Finally, we give examples satisfying our assumptions.