Heterogeneous Differential Privacy via Graphs

TL;DR

This paper extends a graph-based framework for differential privacy, allowing personalized privacy parameters and diverse mechanisms at dataset boundaries, ensuring efficient and utility-optimal privacy guarantees.

Contribution

It introduces a generalized, personalized differential privacy framework on graphs, enabling diverse boundary mechanisms and privacy parameters, with a polynomial-time extension method.

Findings

Efficient polynomial-time mechanism extension for personalized DP.

Framework supports diverse boundary mechanisms and privacy levels.

Ensures utility-optimal privacy guarantees in complex datasets.

Abstract

We generalize a previous framework for designing utility-optimal differentially private (DP) mechanisms via graphs, where datasets are vertices in the graph and edges represent dataset neighborhood. The boundary set contains datasets where an individual's response changes the binary-valued query compared to its neighbors. Previous work was limited to the homogeneous case where the privacy parameter $\varepsilon$ across all datasets was the same and the mechanism at boundary datasets was identical. In our work, the mechanism can take different distributions at the boundary and the privacy parameter $\varepsilon$ is a function of neighboring datasets, which recovers an earlier definition of personalized DP as special case. The problem is how to extend the mechanism, which is only defined at the boundary set, to other datasets in the graph in a computationally efficient and utility optimal manner. Using the concept of strongest induced DP condition we solve this problem efficiently in polynomial time (in the size of the graph).