Robust and Private Bayesian Inference
We examine the robustness and privacy properties of Bayesian inference under assumptions on the prior, but without any modifications to the Bayesian framework. First, 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.
Record created on 2014-03-03, modified on 2016-08-09