Analytic Theory to Differential Privacy
This provides a foundational complement to existing ad hoc and algorithmic approaches in differential privacy, potentially benefiting researchers and practitioners in privacy-preserving data analysis.
The paper tackles the problem of differential privacy by developing a mathematical analysis theory to characterize output correlations across datasets, enabling representation of differentially private mechanisms with minimal parameters and constructing them analytically for almost all query functions.
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.