OAW

Optimal functional supervised classification with separation condition

Gadat, Sébastien, Gerchinovitz, Sebastien and Marteau, Clément (2019) Optimal functional supervised classification with separation condition. Bernoulli journal. (In Press)

This is the latest version of this item.

[img]
Preview
Text
Download (804kB) | Preview
Official URL: https://www.tse-fr.eu/sites/default/files/TSE/docu...

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: Article
Language: English
Date: 2019
Refereed: Yes
Subjects: B- ECONOMIE ET FINANCE
Divisions: TSE-R (Toulouse)
Site: UT1
Date Deposited: 01 Oct 2019 13:59
Last Modified: 01 Oct 2019 13:59
["eprint_fieldname_oai_identifier" not defined]: oai:tse-fr.eu:123580
URI: http://publications.ut-capitole.fr/id/eprint/32803

Available Versions of this Item

Actions (login required)

View Item View Item

Downloads

Downloads per month over past year