@techreport{publications25890,
          volume = {18-904},
           month = {March},
          author = {S{\'e}bastien Gadat and Sebastien Gerchinovitz and Cl{\'e}ment Marteau},
          series = {TSE Working Paper},
       booktitle = {TSE Working Paper},
            type = {Working Paper},
         address = {Toulouse},
           title = {Optimal functional supervised classification with separation condition},
       publisher = {TSE Working Paper},
            year = {2018},
     institution = {Universit{\'e} Toulouse 1 Capitole},
             url = {https://publications.ut-capitole.fr/id/eprint/25890/},
        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.}
}