Laboratoire de Mathématiques de Besançon - UMR 6623 CNRS

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15 décembre 2017: 1 événement

  • Séminaires doctorant

    Vendredi 15 décembre 15:15-16:15 - Sushma Kumari - Kyoto University

    Séminaires doctorant : Universal consistency of $k$-NN rule in $\sigma$-finite dimensional metric spaces

    Résumé :
    The $k$-nearest neighbour (NN) rule is one of the important learning rules in machine learning. We start with the definition of the $k$-NN rule and universal consistency. Charles Stone proved the universal consistency of $k$-NN rule. The essential ingredient for Stone’s theorem was the so-called geometric Stone’s lemma but the proof of the geometric Stone’s lemma is restricted to finite dimensional normed spaces only.
    In this work, we try to extend the geometric Stone’s lemma to the $\sigma$-finite dimensional metric spaces and reprove the universal consistency using the generalized Stone’s theorem. Further questions related to this work are also discussed.

    Lieu : 316B

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