TL;DR
This paper introduces Rao differential privacy, a new privacy definition based on information geometry, which maintains the utility of private estimates while improving sequential composition over existing divergence-based definitions.
Contribution
It proposes a novel privacy framework using Rao distance from information geometry, offering better sequential composition properties than traditional divergence-based definitions.
Findings
Rao differential privacy aligns with previous privacy interpretations.
Improves sequential composition results.
Maintains utility of private estimates.
Abstract
Differential privacy (DP) has recently emerged as a definition of privacy to release private estimates. DP calibrates noise to be on the order of an individuals contribution. Due to the this calibration a private estimate obscures any individual while preserving the utility of the estimate. Since the original definition, many alternate definitions have been proposed. These alternates have been proposed for various reasons including improvements on composition results, relaxations, and formalizations. Nevertheless, thus far nearly all definitions of privacy have used a divergence of densities as the basis of the definition. In this paper we take an information geometry perspective towards differential privacy. Specifically, rather than define privacy via a divergence, we define privacy via the Rao distance. We show that our proposed definition of privacy shares the interpretation of…
Peer Reviews
Decision·Submitted to ICLR 2026
This paper has conceptual novelty. To some extent it challenges the existing
Despite the novelty I'm not fully convinced that we should bring such a new definition into the already rich collection of potentially meaningful DP definitions. The paper correctly points out that the previous definitions do not really use metrics, but I don't think that is crucial if we aren't looking for purely rigorous mathematic definitions. All these definitions are still "symmetric" in the sense that the same constraints imposed by privacy need to hold even if we swap $D$ and $D'$. It's a
See detailed comments below
See detailed comments below
* Introduces a novel, geometry-based definition of differential privacy using the Rao distance. * Demonstrates that Rao DP satisfies composition and post-processing properties fundamental to DP. * Provides closed-form derivations for Laplace, Gaussian, and Generalized Gaussian mechanisms.
* Limited empirical or practical validation The paper is entirely theoretical; it does not provide any numerical illustration or simulation to demonstrate the implications of Rao DP in realistic DP tasks (e.g., trade-offs between privacy and utility). Including such an example would make the contribution more compelling. * Comparative discussion lacks depth While the paper claims tighter composition and better interpretability, it does not quantitatively compare the bounds of Rao DP with thos
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