On the Kernel Rule for Function Classification |
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Authors: | C Abraham G Biau B Cadre |
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Institution: | (1) ENSAM-INRA, UMR Biométrie et Analyse des Systèmes, 2 place Pierre Viala, 34060 Montpellier Cedex 1, France;(2) Institut de Mathématiques et de Modélisation de Montpellier, UMR CNRS 5149, Equipe de Probabilités et Statistique, Université Montpellier II, CC 051, Place Eugène Bataillon, 34095 Montpellier Cedex 5, France |
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Abstract: | Let X be a random variable taking values in a function space
, and let Y be a discrete random label with values 0 and 1. We investigate asymptotic properties of the moving window classification
rule based on independent copies of the pair (X,Y). Contrary to the finite dimensional case, it is shown that the moving window classifier is not universally consistent in
the sense that its probability of error may not converge to the Bayes risk for some distributions of (X,Y). Sufficient conditions both on the space
and the distribution of X are then given to ensure consistency. |
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Keywords: | Classification Consistency Kernel rule Metric entropy Universal consistency |
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