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

Tiantian Sun, Juan Zhang

TL;DR

A weighted Jacobi iterative method is developed that utilizes Gaussian process regression for parameter prediction and provides a corresponding convergence analysis, leveraging a function-space decomposition.

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.

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

TL;DR

A weighted Jacobi iterative method is developed that utilizes Gaussian process regression for parameter prediction and provides a corresponding convergence analysis, leveraging a function-space decomposition.

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.
Paper Structure (8 sections, 60 equations, 13 figures, 3 tables, 1 algorithm)

This paper contains 8 sections, 60 equations, 13 figures, 3 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Error bounds for Gaussian process regression
  3. Notation
  4. Proof Framework for the Error Bound of Gaussian Process Regression
  5. Weighted Jacobi Iteration with GPR
  6. Complexity analysis
  7. Numerical Results
  8. Conclusion

Figures (13)

  • Figure : (a) Iteration versus $n$
  • Figure : (a) Iteration versus $n$
  • Figure : (a) $n$ versus $\omega$
  • Figure : (a) Iteration versus $n$
  • Figure : (b) $\log_{10}\text{RRES}$ versus iteration
  • ...and 8 more figures

Theorems & Definitions (10)

  • Definition 2.1: P-A-R-M-2004
  • Definition 2.2: P-A-R-M-2004
  • Definition 2.3: R-1999
  • proof
  • proof
  • proof
  • proof
  • Example 4.1
  • Example 4.2: J-S-Z-2022
  • Example 4.3