Interval-valued regression and classification models in the framework of machine learning

We present a new approach for constructing regression and classification models for interval-valued data. The risk functional is considered under a set of probability distributions, resulting from the application of a chosen inferential method to the data, such that the bounding distributions of the set depend on the regression and classification parameter. Two extreme ('pessimistic' and 'optimistic') strategies of decision making are presented. The method is applicable with many inferential methods and risk functionals. The general theory is presented together with the specific optimisation problems for several scenarios, including the extension of the support vector machine method for interval-valued data.