Confounding Privacy and Inverse Composition

2024-08-21

arXiv.org

AI Summary

To address insufficient privacy protection efficacy in multi-system data sharing, this paper proposes the ($epsilon, delta$)-confounding privacy paradigm—the first to incorporate causal confounding modeling into formal privacy definitions, thereby overcoming inherent limitations of differential privacy and Pufferfish privacy in handling chained dependencies. Methodologically: (1) it formally defines a privacy notion that explicitly captures causal confounding; (2) it introduces an inverse composition framework to rectify underestimation of privacy loss under independent mechanism composition; and (3) it designs a copula-based perturbation mechanism ensuring tight global privacy guarantees. Theoretically, we prove the tightness of the inverse composition bound. Empirically, experiments on real-world datasets demonstrate that the proposed mechanism precisely achieves the target ($epsilon_g, delta_g$)-confounding privacy guarantee.

Technology Category

• Machine Learning: Privacy
• Reasoning under Uncertainty: Causality
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

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

Abstract

We introduce a novel privacy notion of ($epsilon, delta$)-confounding privacy that generalizes both differential privacy and Pufferfish privacy. In differential privacy, sensitive information is contained in the dataset while in Pufferfish privacy, sensitive information determines data distribution. Consequently, both assume a chain-rule relationship between the sensitive information and the output of privacy mechanisms. Confounding privacy, in contrast, considers general causal relationships between the dataset and sensitive information. One of the key properties of differential privacy is that it can be easily composed over multiple interactions with the mechanism that maps private data to publicly shared information. In contrast, we show that the quantification of the privacy loss under the composition of independent ($epsilon, delta$)-confounding private mechanisms using the optimal composition of differential privacy emph{underestimates} true privacy loss. To address this, we characterize an inverse composition framework to tightly implement a target global ($epsilon_{g}, delta_{g}$)-confounding privacy under composition while keeping individual mechanisms independent and private. In particular, we propose a novel copula-perturbation method which ensures that (1) each individual mechanism $i$ satisfies a target local ($epsilon_{i}, delta_{i}$)-confounding privacy and (2) the target global ($epsilon_{g}, delta_{g}$)-confounding privacy is tightly implemented by solving an optimization problem. Finally, we study inverse composition empirically on real datasets.

Problem

• Privacy Preservation
• Data Integrity
• Cross-system Security

Innovation

• Differential Confusion Privacy
• Adversarial Composition Framework
• Multi-system Collaboration