Regularized Kriging: The Support Vectors Method Applied to Kriging

Abstract

We explore the possible advantages of relaxing the universal kriging non-bias condition using the Support Vectors methodology. This leads to a regularized problem with restrictions, in which the objective function is the traditional variance term plus a term that penalises the bias, and whose resolution gives rise to a continuum of solutions for different values of the regularizer, including simple kriging and universal kriging as specific cases.

The analysis also permits the identification of prediction points that will admit slack in the non-bias condition without adversely affecting the prediction.

The simulations conducted demonstrate that when the process mean function is poorly specified and when there is a significant percentage of outliers, regularized kriging tends to improve the results of ordinary kriging. Given the relationship between kriging, regularization networks and Gaussian processes, the same considerations also apply to both the latter techniques.