  We propose the first theoretical and methodological framework for Gaussian
process regression subject to privacy constraints. The proposed method can be
used when a data owner is unwilling to share a high-fidelity supervised
learning model built from their data with the public due to privacy concerns.
The key idea of the proposed method is to add synthetic noise to the data until
the predictive variance of the Gaussian process model reaches a prespecified
privacy level. The optimal covariance matrix of the synthetic noise is
formulated in terms of semi-definite programming. We also introduce the
formulation of privacy-aware solutions under continuous privacy constraints
using kernel-based approaches, and study their theoretical properties. The
proposed method is illustrated by considering a model that tracks the
trajectories of satellites.
