Balancing Privacy and Utility in Correlated Data: A Study of Bayesian Differential Privacy

TL;DR

This paper investigates how Bayesian differential privacy can be practically implemented in correlated data settings, providing theoretical guarantees and methods to balance privacy with utility in real-world databases.

Contribution

It introduces a new methodology for adapting differential privacy mechanisms to Bayesian differential privacy in correlated data, with theoretical links and practical utility guarantees.

Findings

BDP mechanisms can be designed to maintain utility in correlated data.

Theoretical links between DP and BDP are established.

Practical evaluations show BDP can be implemented without significant utility loss.

Abstract

Privacy risks in differentially private (DP) systems increase significantly when data is correlated, as standard DP metrics often underestimate the resulting privacy leakage, leaving sensitive information vulnerable. Given the ubiquity of dependencies in real-world databases, this oversight poses a critical challenge for privacy protections. Bayesian differential privacy (BDP) extends DP to account for these correlations, yet current BDP mechanisms indicate notable utility loss, limiting its adoption. In this work, we address whether BDP can be realistically implemented in common data structures without sacrificing utility -- a key factor for its applicability. By analyzing arbitrary and structured correlation models, including Gaussian multivariate distributions and Markov chains, we derive practical utility guarantees for BDP. Our contributions include theoretical links between DP and BDP and a novel methodology for adapting DP mechanisms to meet the BDP requirements. Through evaluations on real-world databases, we demonstrate that our novel theorems enable the design of BDP mechanisms that maintain competitive utility, paving the way for practical privacy-preserving data practices in correlated settings.