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2012 Classification via local multi-resolution projections
Jean-Baptiste Monnier
Electron. J. Statist. 6(none): 382-420 (2012). DOI: 10.1214/12-EJS677

Abstract

We focus on the supervised binary classification problem, which consists in guessing the label Y associated to a co-variate Xd, given a set of n independent and identically distributed co-variates and associated labels (Xi,Yi). We assume that the law of the random vector (X,Y) is unknown and the marginal law of X admits a density supported on a set ${\mathcal{A}}$. In the particular case of plug-in classifiers, solving the classification problem boils down to the estimation of the regression function $\eta(X)=\mathbb {E}[Y|X]$. Assuming first ${\mathcal{A}}$ to be known, we show how it is possible to construct an estimator of η by localized projections onto a multi-resolution analysis (MRA). In a second step, we show how this estimation procedure generalizes to the case where ${\mathcal{A}}$ is unknown. Interestingly, this novel estimation procedure presents similar theoretical performances as the celebrated local-polynomial estimator (LPE). In addition, it benefits from the lattice structure of the underlying MRA and thus outperforms the LPE from a computational standpoint, which turns out to be a crucial feature in many practical applications. Finally, we prove that the associated plug-in classifier can reach super-fast rates under a margin assumption.

Citation

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Jean-Baptiste Monnier. "Classification via local multi-resolution projections." Electron. J. Statist. 6 382 - 420, 2012. https://doi.org/10.1214/12-EJS677

Information

Published: 2012
First available in Project Euclid: 19 March 2012

zbMATH: 1274.62251
MathSciNet: MR2988413
Digital Object Identifier: 10.1214/12-EJS677

Subjects:
Primary: 62G05, 62G08
Secondary: 62H12, 62H30

Rights: Copyright © 2012 The Institute of Mathematical Statistics and the Bernoulli Society

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