<> "The repository administrator has not yet configured an RDF license."^^ . <> . . . "A theoretical framework for supervised learning from regions"^^ . "Supervised learning is investigated, when the data are represented not only by labeled points but also labeled regions of the input space. In the limit case, such\r\nregions degenerate to single points and the proposed approach changes back to the classical learning context. The adopted framework entails the minimization\r\nof a functional obtained by introducing a loss function that involves such regions. An additive regularization term is expressed via differential operators that model\r\nthe smoothness properties of the desired input/output relationship. Representer\r\ntheorems are given, proving that the optimization problem associated to learning\r\nfrom labeled regions has a unique solution, which takes on the form of a linear\r\ncombination of kernel functions determined by the differential operators together\r\nwith the regions themselves. As a relevant situation, the case of regions given\r\nby multi-dimensional intervals (i.e., “boxes”) is investigated, which models prior\r\nknowledge expressed by logical propositions."^^ . "2013" . . . "Elsevier"^^ . . . "Neurocomputing"^^ . . . "09252312" . . . . . . . . . . . . . . . . "Marcello"^^ . "Sanguineti"^^ . "Marcello Sanguineti"^^ . . "Giorgio"^^ . "Gnecco"^^ . "Giorgio Gnecco"^^ . . "Marco"^^ . "Gori"^^ . "Marco Gori"^^ . . "Stefano"^^ . "Melacci"^^ . "Stefano Melacci"^^ . . . . . . "A theoretical framework for supervised learning from regions (PDF)"^^ . . . . . "Neurocomputing_Preprint_Gnecco.pdf"^^ . . . "A theoretical framework for supervised learning from regions (Other)"^^ . . . . . . "lightbox.jpg"^^ . . . "A theoretical framework for supervised learning from regions (Other)"^^ . . . . . . "preview.jpg"^^ . . . "A theoretical framework for supervised learning from regions (Other)"^^ . . . . . . "medium.jpg"^^ . . . "A theoretical framework for supervised learning from regions (Other)"^^ . . . . . . "small.jpg"^^ . . "HTML Summary of #1729 \n\nA theoretical framework for supervised learning from regions\n\n" . "text/html" . . . "QA75 Electronic computers. Computer science"@en . .