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.

提出了第一个在隐私约束下进行高斯过程回归的理论和方法框架，其中关键思想是通过添加合成噪声，直到高斯过程模型的预测方差达到预定的隐私水平，来对数据进行保护，并使用半定编程来制定合成噪声的最优协方差矩阵格式，此框架还通过考虑跟踪卫星轨迹的模型进行了说明。