  A continuing challenge for machine learning is providing methods to perform
computation on data while ensuring the data remains private. In this paper we
build on the provable privacy guarantees of differential privacy which has been
combined with Gaussian processes through the previously published
\emph{cloaking method}. In this paper we solve several shortcomings of this
method, starting with the problem of predictions in regions with low data
density. We experiment with the use of inducing points to provide a sparse
approximation and show that these can provide robust differential privacy in
outlier areas and at higher dimensions. We then look at classification, and
modify the Laplace approximation approach to provide differentially private
predictions. We then combine this with the sparse approximation and demonstrate
the capability to perform classification in high dimensions. We finally explore
the issue of hyperparameter selection and develop a method for their private
selection. This paper and associated libraries provide a robust toolkit for
combining differential privacy and GPs in a practical manner.
