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

Optimal functional supervised classification with separation condition