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A Theoretical Framework for Supervised Learning from Regions

Gnecco, Giorgio and Gori, Marco and Melacci, Stefano and Sanguineti, Marcello A Theoretical Framework for Supervised Learning from Regions. Neurocomputing, 129. pp. 25-32. ISSN 0925-2312 (2014)

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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 regions degenerate to single points and the proposed approach changes back to the classical learning context. The adopted framework entails the minimization of a functional obtained by introducing a loss function that involves such regions. An additive regularization term is expressed via differential operators that model the smoothness properties of the desired input/output relationship. Representer theorems are given, proving that the optimization problem associated to learning from labeled regions has a unique solution, which takes on the form of a linear combination of kernel functions determined by the differential operators together with the regions themselves. As a relevant situation, the case of regions given by multi-dimensional intervals (i.e., “boxes”) is investigated, which models prior knowledge expressed by logical propositions.

Item Type: Article
Identification Number: 10.1016/j.neucom.2012.06.065
Additional Information: Available online 25 October 2013
Uncontrolled Keywords: supervised learning; kernel machines; propositional rules; variational calculus; infinite-dimensional optimization; representer theorems
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Research Area: Computer Science and Applications
Depositing User: Giorgio Gnecco
Date Deposited: 17 Sep 2013 13:02
Last Modified: 05 Mar 2014 15:34
URI: http://eprints.imtlucca.it/id/eprint/1794

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