# Principal component analysis for Gaussian process posteriors

arXiv: https://arxiv.org/abs/2107.07115 · HTML: https://mlsanity.com/paper/2107.07115/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 32 references that are in the map.
- First posted on arXiv 15 Jul 2021.

## Builds on (most cited first, 7 of 7)

- [Meta-Learning in Neural Networks: A Survey](https://mlsanity.com/paper/2004.05439/) (2020)
- [When Gaussian Process Meets Big Data: A Review of Scalable GPs](https://mlsanity.com/paper/1807.01065/) (2018)
- [A Survey of Deep Meta-Learning](https://mlsanity.com/paper/2010.03522/) (2020)
- [PACOH: Bayes-Optimal Meta-Learning with PAC-Guarantees](https://mlsanity.com/paper/2002.05551/) (2020)
- [An elementary introduction to information geometry](https://mlsanity.com/paper/1808.08271/) (2018)
- [Transferring Knowledge across Learning Processes](https://mlsanity.com/paper/1812.01054/) (2018)
- [Meta-Learning Mean Functions for Gaussian Processes](https://mlsanity.com/paper/1901.08098/) (2019)

## Built on by (most cited first, 1 of 1)

- [Geometry of EM and related iterative algorithms](https://mlsanity.com/paper/2209.01301/) (2022)

## Abstract (arXiv)

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.