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Information-theoretic (IT) measures based on $f$-divergences have recentlygained interest as a measure of privacy leakage as they allow for trading offprivacy against utility using only a single-value characterization. However,their operational interpretations in the privacy context are unclear. In thispaper, we relate the notion of probabilistic information privacy (IP) toseveral IT privacy metrics based on $f$-divergences. We interpret probabilisticIP under both the detection and estimation frameworks and link it todifferential privacy, thus allowing a precise operational interpretation ofthese IT privacy metrics. We show that the $\chi^2$-divergence privacy metricis stronger than those based on total variation distance and Kullback-Leiblerdivergence. Therefore, we further develop a data-driven empirical riskframework based on the $\chi^2$-divergence privacy metric and realized usingdeep neural networks. This framework is agnostic to the adversarial attackmodel. Empirical experiments demonstrate the efficacy of our approach.

On the Relationship Between Information-Theoretic Privacy Metrics And Probabilistic Information Privacy