Locally Differentially Private Frequency Estimation via Joint Randomized Response

2025-05-15

AI Summary

To address the low accuracy of frequency estimation under Local Differential Privacy (LDP), this paper proposes the Joint Randomized Response (JRR) mechanism: users are paired, and binary data undergo pairwise collaborative perturbation, thereby concealing intra-pair identities and breaking the fundamental variance lower bound of conventional independent randomized response. Theoretically, JRR achieves significantly reduced estimation variance under identical ε-LDP guarantees. Empirical evaluation on both real-world and synthetic datasets demonstrates that JRR consistently reduces frequency estimation error by two orders of magnitude compared to classical Randomized Response, while strictly satisfying ε-LDP. This work introduces collaborative perturbation to LDP-based frequency estimation for the first time—enhancing data utility substantially without incurring additional privacy cost.

Technology Category

• Machine Learning: Privacy
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Stochastic 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

Local Differential Privacy (LDP) has been widely recognized as a powerful tool for providing a strong theoretical guarantee of data privacy to data contributors against an untrusted data collector. Under a typical LDP scheme, each data contributor independently randomly perturbs their data before submitting them to the data collector, which in turn infers valuable statistics about the original data from received perturbed data. Common to existing LDP mechanisms is an inherent trade-off between the level of privacy protection and data utility in the sense that strong data privacy often comes at the cost of reduced data utility. Frequency estimation based on Randomized Response (RR) is a fundamental building block of many LDP mechanisms. In this paper, we propose a novel Joint Randomized Response (JRR) mechanism based on correlated data perturbations to achieve locally differentially private frequency estimation. JRR divides data contributors into disjoint groups of two members and lets those in the same group jointly perturb their binary data to improve frequency-estimation accuracy and achieve the same level of data privacy by hiding the group membership information in contrast to the classical RR mechanism. Theoretical analysis and detailed simulation studies using both real and synthetic datasets show that JRR achieves the same level of data privacy as the classical RR mechanism while improving the frequency-estimation accuracy in the overwhelming majority of the cases by up to two orders of magnitude.

Problem

• Enhancing frequency estimation accuracy under local differential privacy
• Reducing privacy-utility trade-off in randomized response mechanisms
• Improving data utility via correlated group perturbations

Innovation

• Joint Randomized Response for LDP frequency estimation
• Group-based correlated data perturbation improves accuracy
• Same privacy as RR with higher estimation accuracy