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

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.