Tight conditions for consistent variable selection in high dimensional nonparametric regression

Laëtitia Comminges 1, 2 Arnak S. Dalalyan 1, 2
2 IMAGINE [Marne-la-Vallée]
LIGM - Laboratoire d'Informatique Gaspard-Monge, CSTB - Centre Scientifique et Technique du Bâtiment, ENPC - École des Ponts ParisTech
Abstract : We address the issue of variable selection in the regression model with very high ambient dimension, \textit{i.e.}, when the number of covariates is very large. The main focus is on the situation where the number of relevant covariates, called intrinsic dimension, is much smaller than the ambient dimension. Without assuming any parametric form of the underlying regression function, we get tight conditions making it possible to consistently estimate the set of relevant variables. These conditions relate the intrinsic dimension to the ambient dimension and to the sample size. The procedure that is provably consistent under these tight conditions is simple and is based on comparing the empirical Fourier coefficients with an appropriately chosen threshold value.
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https://hal.inria.fr/inria-00566721
Contributor : Arnak Dalalyan <>
Submitted on : Thursday, February 17, 2011 - 9:33:50 AM
Last modification on : Thursday, July 5, 2018 - 2:23:42 PM

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  • HAL Id : inria-00566721, version 2
  • ARXIV : 1102.3616

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Laëtitia Comminges, Arnak S. Dalalyan. Tight conditions for consistent variable selection in high dimensional nonparametric regression. COLT - 24th Conference on Learning Theory - 2011, Jul 2011, Budapest, Hungary. 19 p. ⟨inria-00566721v2⟩

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