Chernoff information as a privacy constraint for adversarial classification and membership advantage

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 and adversary's membership advantage. 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. In this work, we focus on the relationship between the best error exponent of the average error probability and $varepsilon-$ differential privacy. Accordingly, we re-derive Chernoff differential privacy in terms of $varepsilon-$differential privacy via the Radon-Nikodym derivative and show that it satisfies the composition property. Subsequently, we present numerical evaluation results, which demonstrates that Chernoff information outperforms Kullback-Leibler divergence as a function of the privacy budget, the impact of the adversary’s attack and global sensitivity for adversarial classification in Laplace mechanisms. Lastly, we introduce a novel upper bound on the adversary's advantage in membership inference attacks and compare its performance against existing ones.