%0 Conference Paper
%A Gnecco, Giorgio
%A Gori, Marco
%A Melacci, Stefano
%A Sanguineti, Marcello
%B 44th Conference of Italian Operational Research Society (AIRO 2014)
%C Como, Italy
%D 2014
%F eprints:3133
%K Supervised learning; Kernel machines; Infinite-dimensional optimization; Constrained variational  calculus; Representer theorems.
%P 67
%T Supervised Learning from Regions and Box Kernels
%U http://eprints.imtlucca.it/3133/
%X A supervised learning paradigm is investigated, in which the data are represented by labeled regions of  the input space. This learning model is motivated by real-world applications, such as problems of medical  diagnosis and image categorization. The associated optimization framework entails the minimization of a  functional obtained by introducing a loss function that involves the labeled regions. A regularization term  expressed via differential operators, modeling smoothness properties of the desired input/output relationship,  is included. It is shown that the optimization problem associated to supervised learning from regions has  a unique solution, represented as a linear combination of kernel functions determined by the differential  operators together with the regions themselves. The case of regions given by multi-dimensional intervals (i.e.,  “boxes”) is investigated as an interesting instance of learning from regions, which models prior knowledge  expressed by logical propositions. The proposed approach covers as a particular case the classical learning  context, which corresponds to the situation where regions degenerate to single points. Applications and  numerical examples are discussed.