Tight conditions for consistent variable selection in high dimensional nonparametric regression

Laëtitia Comminges, Arnak S. Dalalyan
Proceedings of the 24th Annual Conference on Learning Theory, PMLR 19:187-206, 2011.

Abstract

We address the issue of variable selection in the regression model with very high ambient dimension, 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v19-comminges11a, title = {Tight conditions for consistent variable selection in high dimensional nonparametric regression}, author = {Comminges, Laëtitia and Dalalyan, Arnak S.}, booktitle = {Proceedings of the 24th Annual Conference on Learning Theory}, pages = {187--206}, year = {2011}, editor = {Kakade, Sham M. and von Luxburg, Ulrike}, volume = {19}, series = {Proceedings of Machine Learning Research}, address = {Budapest, Hungary}, month = {09--11 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v19/comminges11a/comminges11a.pdf}, url = {https://proceedings.mlr.press/v19/comminges11a.html}, abstract = {We address the issue of variable selection in the regression model with very high ambient dimension, 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.} }
Endnote
%0 Conference Paper %T Tight conditions for consistent variable selection in high dimensional nonparametric regression %A Laëtitia Comminges %A Arnak S. Dalalyan %B Proceedings of the 24th Annual Conference on Learning Theory %C Proceedings of Machine Learning Research %D 2011 %E Sham M. Kakade %E Ulrike von Luxburg %F pmlr-v19-comminges11a %I PMLR %P 187--206 %U https://proceedings.mlr.press/v19/comminges11a.html %V 19 %X We address the issue of variable selection in the regression model with very high ambient dimension, 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.
RIS
TY - CPAPER TI - Tight conditions for consistent variable selection in high dimensional nonparametric regression AU - Laëtitia Comminges AU - Arnak S. Dalalyan BT - Proceedings of the 24th Annual Conference on Learning Theory DA - 2011/12/21 ED - Sham M. Kakade ED - Ulrike von Luxburg ID - pmlr-v19-comminges11a PB - PMLR DP - Proceedings of Machine Learning Research VL - 19 SP - 187 EP - 206 L1 - http://proceedings.mlr.press/v19/comminges11a/comminges11a.pdf UR - https://proceedings.mlr.press/v19/comminges11a.html AB - We address the issue of variable selection in the regression model with very high ambient dimension, 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. ER -
APA
Comminges, L. & Dalalyan, A.S.. (2011). Tight conditions for consistent variable selection in high dimensional nonparametric regression. Proceedings of the 24th Annual Conference on Learning Theory, in Proceedings of Machine Learning Research 19:187-206 Available from https://proceedings.mlr.press/v19/comminges11a.html.

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