Differential Privacy for Functions and Functional Data

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.

Random Differential Privacy

We propose a relaxed privacy definition called {\em random differential privacy} (RDP). Differential privacy requires that adding any new observation to a database will have small effect on the output of the data-release procedure. Random differential privacy requires that adding a {\em randomly drawn new observation} to a database will have small effect on the output. We show an analog of the composition property of differentially private procedures which applies to our new definition. We show how to release an RDP histogram and we show that RDP histograms are much more accurate than histograms obtained using ordinary differential privacy. We finally show an analog of the global sensitivity framework for the release of functions under our privacy definition.