This paper proposes an extension of principal component analysis for Gaussian process (GP) posteriors, denoted by GP-PCA. Since GP-PCA estimates a low-dimensional space of GP posteriors, it can be used for meta-learning, which is a framework for improving the performance of target tasks by estimating a structure of a set of tasks. The issue is how to define a structure of a set of GPs with an infinite-dimensional parameter, such as coordinate system and a divergence. In this study, we reduce the infiniteness of GP to the finite-dimensional case under the information geometrical framework by considering a space of GP posteriors that have the same prior. In addition, we propose an approximation method of GP-PCA based on variational inference and demonstrate the effectiveness of GP-PCA as meta-learning through experiments.

翻译：本文提出了针对高斯过程后验的主成分分析的扩展方法，记为GP-PCA。由于GP-PCA能够估计高斯过程后验的低维空间，因此可用于元学习——一种通过估计任务集的结构来提升目标任务性能的框架。核心问题在于如何定义具有无限维参数（如坐标系和散度）的高斯过程集合的结构。本研究在信息几何框架下，通过考虑具有相同先验的高斯过程后验空间，将高斯过程的无限维问题降为有限维情形。此外，我们提出了一种基于变分推断的GP-PCA近似方法，并通过实验验证了GP-PCA作为元学习方法的有效性。