On the Privacy-Utility Trade-Off With and Without Direct Access to the Private Data
Amirreza Zamani, Tobias J. Oechtering, Mikael Skoglund · IEEE Transactions on Information Theory · 2023
We study an information theoretic privacy mechanism design problem for two scenarios where the private data is either observable or hidden. In the hidden private data scenario, an agent observes useful dataYthat is correlated with private dataX, and generate disclosed dataUwhich maximizes the revealed information aboutYwhile satisfying a bounded privacy leakage constraint. Considering the other scenario, the agent has additional access toX. To design the privacy mechanism, we first extend the Functional Representation Lemma and Strong Functional Representation Lemma by relaxing the independence condition and thereby allowing a certain leakage. We then find lower and upper bounds on the privacy-utility trade-offs in both scenarios. In particular, for the case where no leakage is allowed andXis observable, our upper and lower bounds improve previous bounds. Considering bounded mutual information as privacy constraint and the observable private data scenario we show that if the common information and mutual information betweenXandYare equal, then the attained upper bound is tight. Finally, the privacy-utility trade-off with prioritized private data is studied where part ofXis more private than the remaining part.