Principal Component Analysis for Gaussian Process Posteriors.

Area of Science:

• Machine Learning
• Statistical Modeling
• Computational Statistics

Background:

• Gaussian Processes (GPs) are powerful non-parametric models but present challenges due to their infinite-dimensional parameter space.
• Meta-learning aims to improve model performance on new tasks by leveraging knowledge from a set of related tasks.
• Defining a structure or divergence for a collection of GPs is complex, hindering their application in meta-learning frameworks.

Purpose of the Study:

• To propose an extension of Principal Component Analysis (PCA) for Gaussian Process (GP) posteriors, termed GP-PCA.
• To address the challenge of defining a structure for infinite-dimensional GP parameters within an information geometrical framework.
• To demonstrate the utility of GP-PCA as a meta-learning approach for enhancing task performance.

Main Methods:

• Developed GP-PCA by reducing the infinite-dimensional GP parameter space to a finite-dimensional one.
• Utilized an information geometrical framework by considering the space of GP posteriors with a shared prior.
• Proposed a variational inference-based approximation method for GP-PCA.

Main Results:

• Successfully reduced the complexity of GP posteriors to a manageable finite-dimensional representation.
• GP-PCA effectively captures the underlying structure within a set of GP posteriors.
• Experimental results validated the effectiveness of GP-PCA as a meta-learning technique.

Conclusions:

• GP-PCA provides a novel method for structuring Gaussian Process posteriors.
• The proposed approach enables the application of GPs in meta-learning by managing their infinite dimensionality.
• GP-PCA shows significant promise for improving performance across various target tasks through effective meta-learning.