Empirical Kriging models and their applications to QSAR

A general Kriging model consists of two additive components: a parametric term and a stochastic error process. It is known that Kriging is an interpolating predictor and allows for a better fit to the data, but suffers from a decreasing ability to generalize to unseen data. By incorporating a disturbing or an independent random error term into Kriging model, the resulting model, which is called empirical Kriging model in the literature, may provide more accurate prediction for the highly noisy data than the Kriging model. This paper presents an extensive survey of the empirical Kriging model for quantitative structure-activity relationship (QSAR) research and extends the parameters estimation technique with highly efficiency. In addiction, QSAR models are established by combining Kriging model or empirical Kriging model with principal components regression (PCR) and partial least squares regression (PLSR). We demonstrate for the real data set that the suggested empirical Kriging model can significantly improve the prediction ability of some commonly used models, including the Kriging model.