Rao Differential Privacy

Carlos J Soto

Keywords: Differential Privacy, Information Geometry, Rao metric

TL;DR: Rather than use divergences to define differential privacy, we introduce the first distance metric based definition of DP via the Rao metric.

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 individual's contribution. Due to 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 previous definitions of privacy while improving on sequential composition.

Primary Area: alignment, fairness, safety, privacy, and societal considerations

Submission Number: 1679