References & Citations
Computer Science > Information Theory
Title: Total Variation Meets Differential Privacy
(Submitted on 2 Nov 2023 (v1), last revised 29 Apr 2024 (this version, v2))
Abstract: The framework of approximate differential privacy is considered, and augmented by leveraging the notion of ``the total variation of a (privacy-preserving) mechanism'' (denoted by $\eta$-TV). With this refinement, an exact composition result is derived, and shown to be significantly tighter than the optimal bounds for differential privacy (which do not consider the total variation). Furthermore, it is shown that $(\varepsilon,\delta)$-DP with $\eta$-TV is closed under subsampling. The induced total variation of commonly used mechanisms are computed. Moreover, the notion of total variation of a mechanism is studied in the local privacy setting and privacy-utility tradeoffs are investigated. In particular, total variation distance and KL divergence are considered as utility functions and studied through the lens of contraction coefficients. Finally, the results are compared and connected to the locally differentially private setting.
Submission history
From: Elena Ghazi [view email][v1] Thu, 2 Nov 2023 19:13:17 GMT (5513kb,D)
[v2] Mon, 29 Apr 2024 15:47:54 GMT (2158kb,D)
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