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Journal Articles Bernoulli Year : 2020

Optimal functional supervised classification with separation condition

Abstract

We consider the binary supervised classification problem with the Gaussian functional model introduced in Cadre [9]. 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 Chaudhuri and Dasgupta [12] and Gadat et al. [18] we also derive a logarithmic lower bound showing that the popular k-nearest neighbors classifier is far from optimality in this specific functional setting.
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Dates and versions

hal-01679648 , version 1 (10-01-2018)
hal-01679648 , version 2 (26-08-2020)

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Sébastien Gadat, Sébastien Gerchinovitz, Clément Marteau. Optimal functional supervised classification with separation condition. Bernoulli, 2020, 26 (3), pp.1797-1831. ⟨10.3150/19-BEJ1170⟩. ⟨hal-01679648v2⟩
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