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Supervised Learning from Regions and Box Kernels

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)

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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.

Item Type: Conference or Workshop Item (Paper)
Uncontrolled Keywords: Supervised learning; Kernel machines; Infinite-dimensional optimization; Constrained variational calculus; Representer theorems.
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Research Area: Computer Science and Applications
Depositing User: Caterina Tangheroni
Date Deposited: 26 Feb 2016 15:06
Last Modified: 26 Feb 2016 15:09
URI: http://eprints.imtlucca.it/id/eprint/3133

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