{"type":"ScholarlyArticle","title":"Analogy-preserving functions: A way to extend Boolean samples","authors":[{"name":"Miguel Couceiro","slug":"miguel-couceiro","given":"Miguel","family":"Couceiro","affiliation":". LORIA , University of Lorraine , Vandoeuvre-lès-Nancy , France"},{"name":"Nicolas Hug","slug":"nicolas-hug","given":"Nicolas","family":"Hug","affiliation":". IRIT , University of Toulouse , France"},{"name":"Henri Prade","slug":"henri-prade","given":"Henri","family":"Prade","affiliation":". IRIT , University of Toulouse , France; . QCIS , University of Technology , Sydney , Australia"},{"name":"Gilles Richard","slug":"gilles-richard","given":"Gilles","family":"Richard","affiliation":". IRIT , University of Toulouse , France; . BITE , London , UK"}],"abstract":"Training set extension is an important issue in machine learning.  Indeed when the examples at hand are in a limited quantity, the performances of standard  classifiers  may  significantly  decrease  and  it can be helpful to build additional examples. In this paper,  we  consider  the  use  of  analogical  reasoning, and more particularly of analogical proportions for extending training sets.  Here the ground truth labels  are  considered  to  be  given  by  a  (partially known) function.  We examine the conditions that are required for such functions to ensure an error-free extension in a Boolean setting. To this end, we introduce  the  notion  of  Analogy  Preserving  (AP) functions, and we prove that their class is the class of  affine  Boolean  functions.   This  noteworthy  theoretical result is complemented with an empirical investigation of approximate AP functions, which suggests that they remain suitable for training set extension.","doi":"10.24963/ijcai.2017/218","url":"https://ijcai.org/proceedings/2017/218","pdf":"https://ijcai.org/proceedings/2017/0218.pdf","markdown":"https://ijcai.org/proceedings/2017/218.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/218","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Machine Learning A-R","track":"Main track","number":218,"pages":{"first":1575,"last":1581},"keywords":["Machine Learning: Machine Learning","Machine Learning: New Problems","Machine Learning: Classification"],"videos":[],"references":[{"position":1,"raw":"[Bayoudh et al., 2007a] S. 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