Membership privacy

We introduce a novel privacy framework that we call Membership Privacy. The framework includes positive membership privacy, which prevents the adversary from significantly increasing its ability to conclude that an entity is in the input dataset, and negative membership privacy, which prevents leaking of non-membership. These notions are parameterized by a family of distributions that captures the adversary's prior knowledge. The power and flexibility of the proposed framework lies in the ability to choose different distribution families to instantiate membership privacy. Many privacy notions in the literature are equivalent to membership privacy with interesting distribution families, including differential privacy, differential identifiability, and differential privacy under sampling. Casting these notions into the framework leads to deeper understanding of the strengthes and weaknesses of these notions, as well as their relationships to each other. The framework also provides a principled approach to developing new privacy notions under which better utility can be achieved than what is possible under differential privacy.