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 bind the influence of the component which cannot be evaluated due to missing values. A regularization term based on the L₁ norm of the maximal variation is used to obtain a mechanism for structure detection in that context. An efficient implementation using the hierarchical kernel machines framework is elaborated.