Kernel Approximation: From Regression to Interpolation
Lulu Kang, V. Roshan Joseph · SIAM/ASA Journal on Uncertainty Quantification · 2016
In this paper we introduce a new interpolation method, known as kernel interpolation (KI), for modeling the output from expensive deterministic computer experiments. We construct it by repeating a generalized version of the classic Nadaraya--Watson kernel regression an infinite number of times. Although this development is numerical, we are able to provide a statistical framework for KI using a nonstationary Gaussian process. This enables us to quantify the uncertainty in the predictions as well as estimate the unknown parameters in the model using the empirical Bayes method. Through some theoretical arguments and numerical examples, we show that KI has better prediction performance than the popular kriging method in certain situations.