SLDP: Semi-Local Differential Privacy for Density-Adaptive Analytics

2026-02-21

AI Summary

This work addresses the challenge in local differential privacy (LDP) where density-adaptive domain discretization suffers from cumulative privacy loss due to iterative refinement, making it difficult to simultaneously achieve high utility and strong privacy guarantees. To resolve this, the authors propose a semi-local differential privacy (SLDP) framework that decouples privacy cost from the number of iterations. In this framework, users partition their data into privacy regions based on local density, and an honest-but-curious server interactively estimates these regions over a public channel. This approach enables high-resolution grid discretization without incurring additional privacy overhead. By integrating an $(\varepsilon, \delta)$-SLDP mechanism with density-adaptive discretization, the method significantly improves the utility of density estimation on both synthetic and real-world datasets while rigorously preserving privacy guarantees.

Technology Category

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

Application Category

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

Abstract

Density-adaptive domain discretization is essential for high-utility privacy-preserving analytics but remains challenging under Local Differential Privacy (LDP) due to the privacy-budget costs associated with iterative refinement. We propose a novel framework, Semi-Local Differential Privacy (SLDP), that assigns a privacy region to each user based on local density and defines adjacency by the potential movement of a point within its privacy region. We present an interactive $(\varepsilon, δ)$-SLDP protocol, orchestrated by an honest-but-curious server over a public channel, to estimate these regions privately. Crucially, our framework decouples the privacy cost from the number of refinement iterations, allowing for high-resolution grids without additional privacy budget cost. We experimentally demonstrate the framework's effectiveness on estimation tasks across synthetic and real-world datasets.

Problem

• Local Differential Privacy
• Density-Adaptive Discretization
• Privacy Budget
• Domain Discretization
• Privacy-Preserving Analytics

Innovation

• Semi-Local Differential Privacy
• Density-Adaptive Discretization
• Privacy Budget Decoupling
• Interactive LDP Protocol
• High-Utility Analytics