Context-aware Privacy Bounds for Linear Queries

2026-01-06

arXiv.org

AI Summary

This work addresses the excessive noise introduced by traditional differential privacy in linear query settings, which stems from its disregard for data distribution and consequently degrades utility. By leveraging pointwise maximal leakage (PML) and incorporating prior knowledge of the data distribution, the authors develop a context-aware privacy analysis of the Laplace mechanism, yielding a tight privacy bound applicable to general linear queries. This approach overcomes the distribution-agnostic limitation of standard differential privacy, significantly reducing required noise while maintaining rigorous privacy guarantees. Theoretical analysis demonstrates that the proposed privacy bound is strictly tighter than the conventional differential privacy bound, and numerical experiments confirm that integrating prior distributional knowledge enhances data utility without compromising privacy protection.

Technology Category

• Machine Learning: Privacy
• Search and Optimization: Distributed Search
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

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

Abstract

Linear queries, as the basis of broad analysis tasks, are often released through privacy mechanisms based on differential privacy (DP), the most popular framework for privacy protection. However, DP adopts a context-free definition that operates independently of the data-generating distribution. In this paper, we revisit the privacy analysis of the Laplace mechanism through the lens of pointwise maximal leakage (PML). We demonstrate that the distribution-agnostic definition of the DP framework often mandates excessive noise. To address this, we incorporate an assumption about the prior distribution by lower-bounding the probability of any single record belonging to any specific class. With this assumption, we derive a tight, context-aware leakage bound for general linear queries, and prove that our derived bound is strictly tighter than the standard DP guarantee and converges to the DP guarantee as this probability lower bound approaches zero. Numerical evaluations demonstrate that by exploiting this prior knowledge, the required noise scale can be reduced while maintaining privacy guarantees.

Problem

• differential privacy
• linear queries
• context-aware privacy
• pointwise maximal leakage
• privacy-utility tradeoff

Innovation

• context-aware privacy
• linear queries
• pointwise maximal leakage
• differential privacy
• prior distribution