Error Analysis of Parameter Prediction via Gaussian Process Regression and Its Application to Weighted Jacobi Iteration

TL;DR

This paper presents a new theoretical framework for analyzing Gaussian process regression errors and applies it to develop a weighted Jacobi method that uses Gaussian process predictions to enhance convergence speed.

Contribution

It introduces a novel error analysis framework for Gaussian process regression and integrates it into a weighted Jacobi iteration to improve convergence.

Findings

Gaussian process regression significantly accelerates Jacobi convergence.

Theoretical framework enables compatibility with various error bounds.

Experimental results confirm improved convergence speed.

Abstract

In this paper, we introduce a novel theoretical framework for Gaussian process regression error analysis, leveraging a function-space decomposition. Based on this framework, we develop a weighted Jacobi iterative method that utilizes Gaussian process regression for parameter prediction and provide a corresponding convergence analysis. Moreover, the convergence conditions are designed to be compatible with other error bounds, enabling a more general analysis. Experimental results show that the parameters predicted based on Gaussian process regression significantly accelerate the convergence speed of Jacobi iterations.