Maximal variation and missing values for componentwise support vector machines

This paper proposes primal-dual kernel machine classifiers based on worst-case analysis of a finite set of observations including missing values of the inputs. Key ingredients are the use of a componentwise Support Vector Machine (cSVM) and an empirical measure of maximal variation of the components to bound the influence of the component which can not be evaluated due to missing values. A regularization term based on the L, norm of the maximal variation is used to obtain a mechanism for structure detection in that context. An efficient implemtation using the hierarchical kernel machines framework is elaborated.