Training and assessment the generalization ability of interpolation methods

We investigate machine learning methods with a certain kind of decision rule. In particular, inverse-distance method of interpolation, method of interpolation by radial basis functions, the method of multi-dimensional interpolation and approximation, based on the theory of random functions, the last method of interpolation is kriging. This paper shows a method of rapid retraining “model” when adding new data to the existing ones. The term “model” means interpolating or approximating function constructed from the training data. This approach reduces the computational complexity of constructing an updated “model” from $O(n^3)$ to $O(n^2)$. We also investigate the possibility of a rapid assessment of generalizing opportunities “model” on the training set using the method of cross-validation leave-one-out cross-validation, eliminating the major drawback of this approach - the necessity to build a new “model” for each element which is removed from the training set.