On the Improved Rates of Convergence for Mat\'ern-type Kernel Ridge Regression, with Application to Calibration of Computer Models

TL;DR

This paper establishes improved convergence rates for kernel ridge regression under new conditions and applies these findings to enhance the understanding of the Kennedy-O'Hagan calibration method for computer models.

Contribution

It introduces novel conditions that lead to faster convergence rates for kernel ridge regression and applies this to improve calibration of computer simulation models.

Findings

Enhanced convergence rates under new conditions

Theoretical validation of Kennedy-O'Hagan calibration convergence

Better understanding of residual minimization in RKHS

Abstract

Kernel ridge regression is an important nonparametric method for estimating smooth functions. We introduce a new set of conditions, under which the actual rates of convergence of the kernel ridge regression estimator under both the L_2 norm and the norm of the reproducing kernel Hilbert space exceed the standard minimax rates. An application of this theory leads to a new understanding of the Kennedy-O'Hagan approach for calibrating model parameters of computer simulation. We prove that, under certain conditions, the Kennedy-O'Hagan calibration estimator with a known covariance function converges to the minimizer of the norm of the residual function in the reproducing kernel Hilbert space.