Metric geometry of the privacy-utility tradeoff

TL;DR

This paper explores the fundamental limits of privacy-utility tradeoffs in synthetic data sharing using metric privacy, introducing the entropic scale to characterize the geometric aspects influencing this balance.

Contribution

It introduces the entropic scale as a novel metric geometry-based measure to analyze the privacy-accuracy tradeoff in metric privacy frameworks.

Findings

The entropic scale captures multiscale geometric properties affecting privacy-utility balance.

The framework applies to diverse metric spaces, demonstrating its broad applicability.

Abstract

Synthetic data are an attractive concept to enable privacy in data sharing. A fundamental question is how similar the privacy-preserving synthetic data are compared to the true data. Using metric privacy, an effective generalization of differential privacy beyond the discrete setting, we raise the problem of characterizing the optimal privacy-accuracy tradeoff by the metric geometry of the underlying space. We provide a partial solution to this problem in terms of the "entropic scale", a quantity that captures the multiscale geometry of a metric space via the behavior of its packing numbers. We illustrate the applicability of our privacy-accuracy tradeoff framework via a diverse set of examples of metric spaces.