Abstract

The literature now contains a large set of methods to privately estimate parameters from a classical statistical model, or to conduct a data mining or machine learning task. However, little is known about how to perform Bayesian statistics privately. In this talk, I will share my thoughts, and a few results, about ways in which Bayesian modelling could be performed to offer some privacy guarantee. In particular, I will discuss some attempts at sampling from posterior predictive distributions under the constraint of differential privacy (DP). I will also discuss empirical differential privacy, a criterion designed to estimate the DP privacy level offered by a certain Bayesian model, and present some recent results on the meaning and limits of this privacy measure. A lot of what I will present is work in progress, and I am hoping that some of you may want to collaborate with me on this research topic.