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On the `Semantics' of Differential Privacy: A Bayesian Formulation
Differential privacy is a definition of "privacy'" for algorithms that
analyze and publish information about statistical databases. It is often
claimed that differential privacy provides guarantees against adversaries with
arbitrary side information. In this paper, we provide a precise formulation of
these guarantees in terms of the inferences drawn by a Bayesian adversary. We
show that this formulation is satisfied by both "vanilla" differential privacy
as well as a relaxation known as (epsilon,delta)-differential privacy. Our
formulation follows the ideas originally due to Dwork and McSherry [Dwork
2006]. This paper is, to our knowledge, the first place such a formulation
appears explicitly. The analysis of the relaxed definition is new to this
paper, and provides some concrete guidance for setting parameters when using
(epsilon,delta)-differential privacy.Comment: Older version of this paper was titled: "A Note on Differential
Privacy: Defining Resistance to Arbitrary Side Information
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