Analytic Theory to Differential Privacy

TL;DR

This paper develops an analytic mathematical framework for differential privacy, enabling the characterization and construction of private mechanisms with minimal parameters, applicable to a wide range of query functions.

Contribution

It introduces a universal analytic approach to differential privacy, providing a theoretical foundation that complements existing ad hoc and algorithmic methods.

Findings

Characterizes correlations among dataset outputs using analytic tools

Constructs differentially private mechanisms analytically

Applicable to almost all query functions

Abstract

The purpose of this paper is to develop a mathematical analysis theory to solve differential privacy problems. The heart of our approaches is to use analytic tools to characterize the correlations among the outputs of different datasets, which makes it feasible to represent a differentially private mechanism with minimal number of parameters. These results are then used to construct differentially private mechanisms analytically. Furthermore, our approaches are universal to almost all query functions. We believe that the approaches and results of this paper are indispensable complements to the current studies of differential privacy that are ruled by the ad hoc and algorithmic approaches.