||We will have a look at the principles predictability, stability, and computability in the field of support vector machines. Support vector machines (SVMs), well-known in machine learning, play a successful role in classification and regression in many areas of science. In the past three decades, much research has been conducted on the statistical and computational properties of support vector machines and related kernel methods. On the one hand, consistency (predictability) and robustness (stability) of the method are of interest. On the other hand, from an applied point of view, there is interest in a method that can deal with many observations and many features (computability). Since SVMs require a lot of computing power and storage capacity, various possibilities for processing large data sets have been proposed. One of them is called regionalization. It divides the space of declaring variables into possibly overlapping domains in a data driven way and defines the function to predict the output by the formation of locally learnt support vector machines. Another advantage of regionalization should be mentioned.
If the generating distribution in different regions of the input space has different characteristics, learning only one “global” SVM may lead to an imprecise estimate. Locally trained predictors can overcome this problem. It is possible to show that a locally learnt predictor is consistent and robust under assumptions that can be checked by the user of this method.