On the Robustness of Information-Theoretic Privacy Measures and Mechanisms

By Mario Díaz, Hao Wang, Flávio du Pin Calmon, Lalitha Sankar. 2018

58 citations recorded by the source corpus.

Consider a data publishing setting for a dataset composed by both private and non-private features. The publisher uses an empirical distribution, estimated from <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> i.i.d. samples, to design a privacy mechanism which is applied to new fresh samples afterward. In this paper, we study the discrepancy between the privacy-utility guarantees for the empirical distribution, used to design the privacy mechanism, and those for the true distribution, experienced by the privacy mechanism in practice. We first show that, for any privacy mechanism, these discrepancies vanish at speed <inline-formula> <tex-math notation="LaTeX">$O(1/\sqrt {n})$ </tex-math></inline-formula> with high probability. These bounds follow from our main technical results regarding the Lipschitz continuity of the considered information leakage measures. Then we prove that the optimal privacy mechanisms for the empirical distribution approach the corresponding mechanisms for the true distribution as the sample size <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> increases, thereby establishing the statistical consistency of the optimal privacy mechanisms. Finally, we introduce and study <italic>uniform privacy mechanisms</italic> which, by construction, provide privacy to all the distributions within a neighborhood of the estimated distribution and, thereby, guarantee privacy for the true distribution with high probability.

Subfields: Artificial Intelligence, Management Science and Operations Research, Statistics and Probability

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Citations in the corpus

Privacy in Deep Learning: A Survey (2020, background): “There is a body of work studying information-theoretic based methods for both privacy and fairness, where privacy and fairness are provided through information degradation, through obfuscation or adversarial learning and demonstrated by mutual information reduction [67, 68, 48, 69, 70, 71, 72, 73, 7”
Obfuscation via Information Density Estimation (2019, background): “information-theoretic privacy (Calmon and Fawaz, 2012; Asoodeh et al., 2018; Issa et al., 2018; Hsu et al., 2018; Diaz et al., 2018)) or partial (cf.”
The Roadmap to 6G Security and Privacy (2021, background): “Different notions of privacy leakage have been proposed to capture the capacity of adversaries to estimate private information, for example, Shannon’s mutual information, differential privacy, among others [158], as well as different leakage measures.”