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

2025-06-26

AI Summary

Standard differential privacy (DP) underestimates privacy risk in correlated data, while existing Bayesian differential privacy (BDP) mechanisms suffer severe utility degradation. To address this, we propose the first adaptable BDP implementation framework compatible with mainstream DP mechanisms. By establishing a theoretical connection between DP and BDP, we introduce novel adaptive modifications for canonical mechanisms—including the Gaussian and Laplace mechanisms—and derive tight utility bounds for multivariate Gaussian distributions and Markov chains, two representative correlated data structures. Empirical evaluation on real-world databases demonstrates that our mechanisms achieve utility nearly matching standard DP, while providing rigorous BDP guarantees. This significantly improves the privacy–utility trade-off for correlated data scenarios.

Technology Category

• Machine Learning: Privacy
• Reasoning under Uncertainty: Relational Probabilistic Models
• Multiagent Systems: Mechanism Design

Application Category

• Security and Privacy: Data transparency and provenance
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems
• Responsible Web: Data and user privacy-enhancing technologies for the Web

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.

Problem

• Address privacy risks in correlated data under differential privacy
• Reduce utility loss in Bayesian differential privacy mechanisms
• Develop practical BDP mechanisms for real-world data structures

Innovation

• Extends DP to handle correlated data via BDP
• Links DP and BDP with theoretical guarantees
• Adapts DP mechanisms for BDP with utility