Optimization of hyperparameters of Gaussian process regression with the help of а low-order high-dimensional model representation: application to a potential energy surface

When the data are sparse, optimization of hyperparameters kernel in Gaussian process regression by commonly used maximum likelihood estimation (MLE) criterion often leads to overfitting. We show that choosing (in this case, length parameter and regularization parameter) based on a completeness basis corresponding linear problem is superior MLE. facilitated use high-dimensional model representation (HDMR) whereby low-order HDMR can provide reliable reference functions large synthetic test sets needed for even when original few.