  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.
