{"type":"ScholarlyArticle","title":"Behavior of Analogical Inference w.r.t. Boolean Functions","authors":[{"name":"Miguel Couceiro","slug":"miguel-couceiro","given":"Miguel","family":"Couceiro","affiliation":". University of Lorraine , CNRS , Inria , LORIA , F-54000 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"}],"abstract":"It has been observed that a particular form of analogical inference, based on analogical proportions,\r\nyields competitive results in classification tasks.\r\nUsing the algebraic normal form of Boolean functions, it has been shown that analogical prediction\r\nis always exact iff the labeling function is affine.\r\nWe point out that affine functions are also meaningful when using another view of analogy. We address the accuracy of analogical inference for arbitrary Boolean functions and show that if a function\r\nis epsilon-close to an affine function, then the probability\r\nof making a wrong prediction is upper bounded by\r\n4 epsilon. This result is confirmed by an empirical study\r\nshowing that the upper bound is tight. It highlights\r\nthe specificity of analogical inference,\r\nalso characterized in terms of the Hamming distance.","doi":"10.24963/ijcai.2018/284","url":"https://ijcai.org/proceedings/2018/284","pdf":"https://ijcai.org/proceedings/2018/0284.pdf","markdown":"https://ijcai.org/proceedings/2018/284.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/284","volume":{"slug":"2018","title":"Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2018","url":"https://ijcai.org/proceedings/2018/","year":2018,"location":"Stockholm","dates":"13-19 July 2018","editors":"Jérôme Lang","isbn":"978-0-9992411-2-7","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2018"},"section":"Machine Learning","track":"Main track","number":284,"pages":{"first":2057,"last":2063},"keywords":["Knowledge Representation and Reasoning: Qualitative Reasoning","Machine Learning: Classification"],"videos":[],"references":[{"position":1,"raw":"[Bayoudh et al., 2007] S. 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