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.

翻译：我们提出了首个受隐私约束的高斯过程回归理论与方法论框架。该方法适用于数据所有者因隐私顾虑而不愿公开基于其数据构建的高保真有监督学习模型的情形。其核心思想是通过向数据添加合成噪声，直至高斯过程模型的预测方差达到预设的隐私水平。合成噪声的最优协方差矩阵通过半定规划形式化表述。我们还引入了基于核方法的连续隐私约束下隐私感知解决方案的表述，并研究了其理论性质。通过追踪卫星轨迹的模型示例，对所提方法进行了说明。