TY  - CONF
N2  - 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.
M2  - Como, Italy
A1  - Gnecco, Giorgio
A1  - Gori, Marco
A1  - Melacci, Stefano
A1  - Sanguineti, Marcello
UR  - http://www.cnr.it/istituti/Allegato_97592.pdf?LO=01000000d9c8b7a6090000000c000000cbb10000646f9c53000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000&type=application/pdf
Y1  - 2014///
KW  - Supervised learning; Kernel machines; Infinite-dimensional optimization; Constrained variational
calculus; Representer theorems.
TI  - Supervised Learning from Regions and Box Kernels
AV  - none
T2  - 44th Conference of Italian Operational Research Society (AIRO 2014)
ID  - eprints3133
ER  -