Principal component analysis for Gaussian process posteriors
This work addresses a foundational issue in meta-learning for Gaussian processes, but it appears incremental as it extends existing PCA methods to GP posteriors.
The paper tackles the problem of defining a structure for a set of Gaussian process (GP) posteriors with infinite-dimensional parameters by proposing GP-PCA, which reduces this to a finite-dimensional case under an information geometrical framework and includes a variational inference approximation. It demonstrates the effectiveness of GP-PCA for meta-learning through experiments, though no concrete numbers are provided.
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.