eprintid: 3133
rev_number: 7
eprint_status: archive
userid: 69
dir: disk0/00/00/31/33
datestamp: 2016-02-26 15:06:47
lastmod: 2016-02-26 15:09:47
status_changed: 2016-02-26 15:06:47
type: conference_item
metadata_visibility: show
creators_name: Gnecco, Giorgio
creators_name: Gori, Marco
creators_name: Melacci, Stefano
creators_name: Sanguineti, Marcello
creators_id: giorgio.gnecco@imtlucca.it
creators_id: 
creators_id: 
creators_id: 
title: Supervised Learning from Regions and Box Kernels
ispublished: pub
subjects: QA75
divisions: CSA
full_text_status: none
pres_type: paper
keywords: Supervised learning; Kernel machines; Infinite-dimensional optimization; Constrained variational
calculus; Representer theorems.
abstract: 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
date_type: published
pagerange: 67
event_title: 44th Conference of Italian Operational Research Society (AIRO 2014)
event_location: Como, Italy
event_dates: September 2-5, 2014
event_type: conference
refereed: TRUE
book_title: Book of abstracts of the 44th Conference of Italian Operational Research Society (AIRO 2014)
official_url: http://www.cnr.it/istituti/Allegato_97592.pdf?LO=01000000d9c8b7a6090000000c000000cbb10000646f9c53000000000100000000000000000000000000000000000000000000000000000000000000000000000000000000000000&type=application/pdf
citation:   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)