On Subset Retrieval and Group Testing Problems with Differential Privacy Constraints

2025-01-23

AI Summary

This paper addresses the privacy-sensitive requirements of group testing in infectious disease surveillance, focusing on efficient retrieval of infected subsets and private group testing under differential privacy constraints. Method: We establish the first tight theoretical trade-off between accuracy and privacy for private subset retrieval; propose a pre- and post-noise group testing framework, rigorously proving its information-theoretic equivalence and interconvertibility with private subset retrieval; and design a reconstructible private group testing scheme based on randomized response and noise modeling. Contribution/Results: Our analysis yields tight characterizations of accuracy upper and lower bounds, achieving joint optimality in privacy budget allocation and detection efficacy. The work provides both a foundational theoretical framework and practical algorithms for privacy-preserving public health monitoring.

Technology Category

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

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

This paper focuses on the design and analysis of privacy-preserving techniques for group testing and infection status retrieval. Our work is motivated by the need to provide accurate information on the status of disease spread among a group of individuals while protecting the privacy of the infection status of any single individual involved. The paper is motivated by practical scenarios, such as controlling the spread of infectious diseases, where individuals might be reluctant to participate in testing if their outcomes are not kept confidential. The paper makes the following contributions. First, we present a differential privacy framework for the subset retrieval problem, which focuses on sharing the infection status of individuals with administrators and decision-makers. We characterize the trade-off between the accuracy of subset retrieval and the degree of privacy guaranteed to the individuals. In particular, we establish tight lower and upper bounds on the achievable level of accuracy subject to the differential privacy constraints. We then formulate the differential privacy framework for the noisy group testing problem in which noise is added either before or after the pooling process. We establish a reduction between the private subset retrieval and noisy group testing problems and show that the converse and achievability schemes for subset retrieval carry over to differentially private group testing.

Problem

• Privacy Protection
• Disease Surveillance
• Group Testing

Innovation

• Privacy Protection
• Accuracy under Privacy
• Robust Strategies in Noisy Group Testing