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arXiv · 1801.03345

Optimal functional supervised classification with separation condition

Sébastien Gadat·Sébastien Gerchinovitz·Clément Marteau
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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.

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Sébastien Gadat, Sébastien Gerchinovitz, Clément Marteau. 2018-01-10. Optimal functional supervised classification with separation condition. https://arxiv.org/abs/1801.03345

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