Dependency Triad: A Metric to Quantify the Dependencies Between Attributes for Local Differential Privacy

2026-08-04

AI Summary

This work addresses the challenge of quantifying privacy leakage arising from attribute dependencies in multidimensional data under local differential privacy, a setting where existing methods struggle to provide efficient and accurate risk assessment. The paper introduces a novel metric termed the “Dependency Triad,” which models uncertainty in pairwise attribute dependencies through three parameters. This approach enables conservative leakage estimation in constant time without requiring precise prior knowledge of data distributions. Designed to handle high-cardinality and sparse data scenarios, the method supports scalable evaluation of cumulative privacy leakage across multiple dimensions. Empirical evaluations on diverse synthetic and real-world datasets demonstrate that the proposed technique consistently yields stable and accurate estimates of associative privacy leakage, significantly outperforming current state-of-the-art solutions.

Abstract

Collecting multidimensional user data is essential for extracting rich insights across various applications. Local Differential Privacy (LDP) has emerged as a de facto standard for mitigating privacy risks in such scenarios. A key challenge in privacy-preserving multidimensional data collection lies in inter-attribute dependencies, as they can inadvertently reveal correlated information and increase privacy vulnerabilities. Therefore, accurately measuring correlation-induced privacy leakage (CPL) is essential for privacy analysis and privacy-utility trade-off. However, existing CPL analysis solutions either require accurate prior knowledge or face scalability challenges for large numbers of attributes and high-cardinality attributes. These limit their practical applicability in real data. To address this research gap, we propose a novel metric, ``Dependency Triad'' (DT), which summarizes the pairwise dependency information relevant to CPL using three parameters and yields a \emph{constant-time} conservative estimator of pairwise CPL. DT explicitly models uncertainty in prior distributional knowledge through its parameters, delivering robust leakage estimates. Moreover, its robustness to sparse distributions makes it particularly suitable for high-cardinality attributes, while the pairwise formulation serves as a tractable building block for assessing total leakage in multidimensional settings. Extensive experiments on both synthetic and real datasets demonstrate that DT consistently estimates CPL across diverse dependency regimes and prior uncertainties.

Problem

• Local Differential Privacy
• Correlation-Induced Privacy Leakage
• Multidimensional Data Collection
• Attribute Dependencies
• Privacy-Utility Trade-off

Innovation

• Dependency Triad
• Local Differential Privacy
• Correlation-Induced Privacy Leakage
• High-Cardinality Attributes
• Privacy-Utility Trade-off