A type-II maximum-likelihood approach to Gaussian scale mixture-based sparse regression Kriging

Abstract

In this paper, a novel sparse regression Kriging method termed SRK is proposed, putting an emphasis on efficiently identifying an adaptive overall trend. The main idea underlying SRK is that, by applying a Cholesky decomposition on the correlation matrix, a general Gaussian scale mixture prior- based sparse Bayesian learning scheme can be naturally incorporated into Gaussian process regression, thus facilitating determination of the adaptive trend and correlation functions in an iterative manner. In particular, two sparsity-inducing distributions including Laplacian and Student’s T are implemented as special cases of the Gaussian scale mixture prior, and it is found that their influence to SRK just differs in the estimating formula of a common hyper-parameter. Metamodeling experiments are performed on practical engineering design problems with very limited training data points. Results demonstrate that the Laplacian-based SRK is not only more sensible than T-based SRK, but also achieves comparable or even better performance than benchmark approaches in terms of either computational cost or prediction precision.