Privacy-utility tradeoff under statistical uncertainty

We focus on the privacy-accuracy tradeoff encountered by a user who wishes to release some data to an analyst, that is correlated with his private data, in the hope of receiving some utility. We rely on a general statistical inference framework, under which data is distorted before its release, according to a probabilistic privacy mechanism designed under utility constraints. Using recent results on maximal correlation and hyper-contractivity of Markov processes, we first propose novel techniques to design utility-aware privacy mechanisms against inference attacks, when only partial statistical knowledge of the prior distribution linking private data and data to be released is available. We then propose optimal privacy mechanisms in the class of additive noise mechanisms, for both continuous and discrete released data, whose design requires only knowledge of second-order moments of the data to be released. We then turn our attention to multi-agent systems, where multiple data releases occur, and use tensorization results of maximal correlation to analyze how privacy guarantees compose after collusion or composition. Finally, we show the relationship between different existing privacy metrics, in particular divergence privacy, and differential privacy.