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Optimal functional supervised classification with separation condition

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  • Gadat, Sébastien
  • Gerchinovitz, Sebastien
  • Marteau, Clément

Abstract

We consider the binary supervised classification problem with the Gaussian functional model introduced in [7]. Taking advantage of the Gaussian structure, we design a natural plug-in classifier and derive a family of upper bounds on its worst-case excess risk over Sobolev spaces. These bounds are parametrized by a separation distance quantifying the difficulty of the problem, and are proved to be optimal (up to logarithmic factors) through matching minimax lower bounds. Using the recent works of [9] and [14] we also derive a logarithmic lower bound showing that the popular k-nearest neighbors classifier is far from optimality in this specific functional setting.

Suggested Citation

  • Gadat, Sébastien & Gerchinovitz, Sebastien & Marteau, Clément, 2018. "Optimal functional supervised classification with separation condition," TSE Working Papers 18-904, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:32574
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    References listed on IDEAS

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    1. Gérard Biau & Erwan Scornet, 2016. "A random forest guided tour," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 197-227, June.
    2. Gérard Biau & Erwan Scornet, 2016. "Rejoinder on: A random forest guided tour," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(2), pages 264-268, June.
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