relation: http://eprints.imtlucca.it/3133/
title: Supervised Learning from Regions and Box Kernels
creator: Gnecco, Giorgio
creator: Gori, Marco
creator: Melacci, Stefano
creator: Sanguineti, Marcello
subject: QA75 Electronic computers. Computer science
description: 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.
date: 2014
type: Conference or Workshop Item
type: PeerReviewed
identifier:   Gnecco, Giorgio and Gori, Marco and Melacci, Stefano and Sanguineti, Marcello  Supervised Learning from Regions and Box Kernels.  In: 44th Conference of Italian Operational Research Society (AIRO 2014), September 2-5, 2014, Como, Italy p. 67.        (2014)  
relation: http://www.cnr.it/istituti/Allegato_97592.pdf?LO=01000000d9c8b7a6090000000c000000cbb10000646f9c53000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000&type=application/pdf