An imprecise extension of SVM-based machine learning models

Abstract

Abstract A general approach for incorporating imprecise prior knowledge and for robustifying the machine learning SVM-based models is proposed in the paper. The main idea underlying the approach is to use a double duality representation in the framework of the minimax strategy of decision making. This idea allows us to get simple extensions of SVMs including additional constraints for optimization variables (the Lagrange multipliers) formalizing the incorporated imprecise information. The approach is applied to regression, binary classification and one-class classification SVM-based problems. Moreover, it is adopted to set-valued or interval-valued training data. For every problem, numerical examples are provided which illustrate how imprecise information may improve the machine learning algorithm performance.