Regularized Kriging

• Activity Number: 6
• Type: Invited
• Date/Time: Sunday, August 1, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Chein-Yu Peng * and C.F. Jeff Wu+
• Companies: Academia Sinica and Georgia Institute of Technology
• Keywords: computer experiment ; condition number ; ridge regression ; Gaussian process

Abstract

Kriging is a commonly used technique for developing meta-models as surrogates for computationally intensive simulations. One difficulty with kriging is the potential numerical instability in the computation of the inverse of the covariance matrix. This instability can lead to large variability or even unreliability of the kriging predictor. First, we study some causes of ill-conditioning in kriging models. A regularized version of kriging is then proposed to overcome this difficulty. It is particularly useful for computationally intensive simulations with large sample size or input variables. Some asymptotic results on its interpolation bias and mean-squared errors are presented. A simulation study is performed to show the differences between kriging and regularized kriging and to demonstrate the advantages of the latter.