Constructing Gaussian Processes via Samplets

TL;DR

This paper introduces a Samplet-based method for constructing Gaussian Processes that significantly reduces computational complexity, enabling efficient and optimal regression for low-dimensional datasets.

Contribution

It presents a novel Samplet-based approach that decreases Gaussian Process training complexity from cubic to log-linear scale, improving efficiency and model selection.

Findings

Achieves near-optimal convergence rates for Gaussian Process models.

Reduces computational complexity from cubic to log-linear scale.

Enables efficient training and model selection for low-dimensional data.

Abstract

Gaussian Processes face two primary challenges: constructing models for large datasets and selecting the optimal model. This master's thesis tackles these challenges in the low-dimensional case. We examine recent convergence results to identify models with optimal convergence rates and pinpoint essential parameters. Utilizing this model, we propose a Samplet-based approach to efficiently construct and train the Gaussian Processes, reducing the cubic computational complexity to a log-linear scale. This method facilitates optimal regression while maintaining efficient performance.