Differentially Private Response Mechanisms on Categorical Data

TL;DR

This paper develops a theoretical framework for differential privacy mechanisms on categorical data, providing necessary and sufficient conditions, bounds on error, and characterizing optimal mechanisms to enhance privacy guarantees.

Contribution

It introduces the concept of sufficient sets for differential privacy, deriving tight bounds and characterizing optimal mechanisms for finite datasets.

Findings

Derived necessary and sufficient conditions for differential privacy.

Established a tight lower bound on maximal expected error.

Characterized the optimal mechanism minimizing error.

Abstract

We study mechanisms for differential privacy on finite datasets. By deriving \emph{sufficient sets} for differential privacy we obtain necessary and sufficient conditions for differential privacy, a tight lower bound on the maximal expected error of a discrete mechanism and a characterisation of the optimal mechanism which minimises the maximal expected error within the class of mechanisms considered.