Differential Privacy and Private Bayesian Inference.
Christos Dimitrakakis, Blaine A. Nelson, Aikaterini Mitrokotsa, Ben Rubinstein · 2014
We consider a Bayesian statistician (B) communicating with an untrusted third party (A). B wants to convey useful answers to the queries of A, but with-out revealing private information. For example, we may want to give statistics about how many people suffer from a disease, but without revealing whether a particular person has it. This requires us to strike a good balance between utility and privacy. In this extended abstract, we summarise our results on the inherent privacy and robustness properties of Bayesian inference [1]. We formalise and answer the question of whether B can select a prior distribution so that a com-putationally unbounded A cannot obtain private information from queries. Our setting is as follows: (i) B selects a model family (FΘ) and a prior (ξ). (ii) A is allowed to see FΘ and ξ and is computationally unbounded. (iii) B observes data x and calculates the posterior ξpθ|xq but does not reveal it. Instead, B responds to queries at times t “ 1,... as follows. (iv) A sends a query qt to B.