Constructing Gaussian Processes via Samplets
This work addresses scalability issues in Gaussian Processes for low-dimensional data, offering a more efficient method for practitioners, though it is incremental as it builds on existing convergence results.
The thesis tackled the challenges of constructing Gaussian Processes for large datasets and selecting optimal models in low-dimensional cases by proposing a Samplet-based approach, which reduced computational complexity from cubic to log-linear scale, enabling efficient training and optimal regression.
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.