Principal Component Analysis for Gaussian Process Posteriors
Principal Component Analysis for Gaussian Process Posteriors
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DOI：
10.1162/neco_a_01489
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发表时间：
2021-07
影响因子：
2.9
通讯作者：
Hideaki Ishibashi;S. Akaho
中科院分区：
文献类型：
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作者：
Hideaki Ishibashi;S. Akaho
摘要本文提出了一种扩展的高斯过程后验主成分分析方法，称为GP-PCA。由于GP-PCA估计GP后验的低维空间，因此它可以用于元学习，元学习是一种通过估计一组任务的结构来提高目标任务性能的框架。问题是如何定义一组具有无限维参数（如坐标系和散度）的GP的结构。在这项研究中，我们减少了无限的GP的有限维的情况下，信息几何框架下，通过考虑一个空间的GP后验，具有相同的先验。此外，我们提出了一种基于变分推理的GP-PCA近似方法，并通过实验证明了GP-PCA作为元学习的有效性。
Abstract This letter 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 metalearning, 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.