Connections between Kernel Analog Forecasting and Gaussian Process Regression

In this short communication we expose connections between two data-driven machine learning methods, kernel analog forecasting (KAF) and Gaussian process regression (GPR). In particular, it is shown that there are three major points in which KAF differs from GPR: the use of a specific kernel, normalization that guarantees spectrum to lie in $(0, 1]$, and spectral truncation, which acts both as a computational speed-up and regularization.