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Analogy-preserving Functions: A Way to Extend Boolean Samples

Miguel Couceiro 1 Nicolas Hug 2 Henri Prade 2, 3 Gilles Richard 2, 4 
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.
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Submitted on : Tuesday, December 19, 2017 - 9:58:13 PM
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Miguel Couceiro, Nicolas Hug, Henri Prade, Gilles Richard. Analogy-preserving Functions: A Way to Extend Boolean Samples. 26th International Joint Conference on Artificial Intelligence (IJCAI 2017), International Joint Conferences on Artifical Intelligence (IJCAI), Aug 2017, Melbourne, Australia. pp.1-7, ⟨10.24963/ijcai.2017/218⟩. ⟨hal-01668230⟩



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