%S TSE Working Paper
%A Sébastien Gadat
%A Sebastien Gerchinovitz
%A Clément Marteau
%T Optimal functional supervised classification with separation condition
%X 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.
%B TSE Working Paper
%V 18-904
%D 2018
%C Toulouse
%I TSE Working Paper
%L publications25890