📝 SummarXiv

Abstract

This work inspects a privacy metric based on Chernoff information, namely Chernoff differential privacy, due to its significance in characterization of the optimal classifier's performance. Adversarial classification, as any other classification problem is built around minimization of the (average or correct detection) probability of error in deciding on either of the classes in the case of binary classification. Unlike the classical hypothesis testing problem, where the false alarm and mis-detection probabilities are handled separately resulting in an asymmetric behavior of the best error exponent, in this work, we characterize the relationship between $\varepsilon\textrm{-}$differential privacy, the best error exponent of one of the errors (when the other is fixed) and the best average error exponent. Accordingly, we re-derive Chernoff differential privacy in connection with $\varepsilon\textrm{-}$differential privacy using the Radon-Nikodym derivative, and prove its relation with Kullback-Leibler (KL) differential privacy. Subsequently, we present numerical evaluation results, which demonstrates that Chernoff information outperforms Kullback-Leibler divergence as a function of the privacy parameter $\varepsilon$ and the impact of the adversary's attack in Laplace mechanisms. Lastly, we introduce a new upper bound on adversary's membership advantage in membership inference attacks using Chernoff DP and numerically compare its performance with existing alternatives based on $(\varepsilon, \delta)\textrm{-}$differential privacy in the literature.