Differential privacy is a framework for privately releasing summaries of a database. Previous work has focused mainly on methods for which the output is a finite dimensional vector, or an element of some discrete set. We develop methods for releasing functions while preserving differential privacy. Specifically, we show that adding an appropriate Gaussian process to the function of interest yields differential privacy. When the functions lie in the same RKHS as the Gaussian process, then the correct noise level is established by measuring the "sensitivity" of the function in the RKHS norm. As examples we consider kernel density estimation, kernel support vector machines, and functions in reproducing kernel Hilbert spaces.
Hall et al. REF study how to preserve ( , δ)-differential privacy for releasing (infinite dimensional) functions, and show that adding Gaussian process noise to the released function can preserve ( , δ)-differential privacy.
Differential Privacy for Functions and Functional Data
ArXiv
ArXiv
Mathematics Computer Science