Function Privatization in the Local Model

2026-07-29

AI Summary

This work addresses the utility degradation commonly observed in local differential privacy (LDP) when publishing functional data, such as trajectories or density curves, due to excessive perturbation. It introduces Geo-Privacy into the local model for the first time, adaptively calibrating privacy guarantees based on the distance between functions: stronger protection is provided for nearby functions, while sufficiently distant functions remain distinguishable. This approach overcomes the utility bottleneck inherent in conventional LDP mechanisms for releasing continuous functions. By integrating continuous function modeling with an efficient perturbation strategy, the proposed mechanism demonstrably enhances data utility while preserving strong privacy for neighboring functions, as validated across multiple real-world datasets.

Abstract

We study the problem of privately releasing functions, with a particular focus on curves, which are images of continuous functions on some finite interval. Many types of data exist naturally as curves, such as trajectory data or $1$D density curves. We shall primarily be interested in the local model setting, where the function to be privatized captures data belonging to one individual, which is the more challenging setting with limited prior work. Under the standard notion of local differential privacy (DP), any two arbitrarily different functions are required to be made indistinguishable by privatization, which is too strong to allow meaningful utility; we thus work with a generalized notion of DP known as Geo-Privacy (GP), which allows functions far apart to be distinguished more easily while providing strong protection for near functions. To demonstrate the effectiveness of our framework, we provide experimental evaluation on several datasets.

Problem

• Function Privatization
• Local Differential Privacy
• Curves
• Geo-Privacy
• Private Data Release

Innovation

• Local Differential Privacy
• Function Privatization
• Geo-Privacy
• Curve Data
• Privacy-Utility Tradeoff