Optimal functional supervised classification with separation condition

Gadat, Sébastien, Gerchinovitz, Sebastien and Marteau, Clément (2018) Optimal functional supervised classification with separation condition. TSE Working Paper, n. 18-904, Toulouse

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Official URL: http://tse-fr.eu/pub/32574

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.

Item Type: Monograph (Working Paper)
Language: English
Date: March 2018
Place of Publication: Toulouse
Subjects: B- ECONOMIE ET FINANCE
Divisions: TSE-R (Toulouse)
Institution: Université Toulouse 1 Capitole
Site: UT1
Date Deposited: 24 Apr 2018 11:23
Last Modified: 24 Apr 2018 11:23
OAI ID: oai:tse-fr.eu:32574
URI: http://publications.ut-capitole.fr/id/eprint/25890

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