On the Robustness of Information-Theoretic Privacy Measures and Mechanisms
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Consider a data publishing setting for a dataset composed of non-private features correlated with a set of private features not necessarily present in the dataset. The objective of the publisher is to maximize the amount of information about the non-private features in a revealed dataset (utility), while keeping the information leaked about the private attributes bounded (privacy). Here, both privacy and utility are measured using information leakage measures that arise in adversarial settings. We consider a practical setting wherein the publisher uses an estimate of the joint distribution of the features to design the privacy mechanism. For any privacy mechanism, we provide probabilistic upper bounds for the discrepancy between the privacy guarantees for the empirical and true distributions, and similarly for utility. These bounds follow from our main technical results regarding the Lipschitz continuity of the considered information leakage measures. We also establish the statistical consistency of the notion of optimal privacy mechanism. Finally, we introduce and study the family of uniform privacy mechanisms, mechanisms designed upon an estimate of the joint distribution which are capable of providing privacy to a whole neighborhood of the estimated distribution, and thereby, guaranteeing privacy for the true distribution with high probability.
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