Open Access
Translator Disclaimer
2008 LASSO, Iterative Feature Selection and the Correlation Selector: Oracle inequalities and numerical performances
Pierre Alquier
Electron. J. Statist. 2: 1129-1152 (2008). DOI: 10.1214/08-EJS288

Abstract

We propose a general family of algorithms for regression estimation with quadratic loss, on the basis of geometrical considerations. These algorithms are able to select relevant functions into a large dictionary. We prove that a lot of methods that have already been studied for this task (LASSO, Dantzig selector, Iterative Feature Selection, among others) belong to our family, and exhibit another particular member of this family that we call Correlation Selector in this paper. Using general properties of our family of algorithm we prove oracle inequalities for IFS, for the LASSO and for the Correlation Selector, and compare numerical performances of these estimators on a toy example.

Citation

Download Citation

Pierre Alquier. "LASSO, Iterative Feature Selection and the Correlation Selector: Oracle inequalities and numerical performances." Electron. J. Statist. 2 1129 - 1152, 2008. https://doi.org/10.1214/08-EJS288

Information

Published: 2008
First available in Project Euclid: 21 November 2008

zbMATH: 1320.62084
MathSciNet: MR2460860
Digital Object Identifier: 10.1214/08-EJS288

Subjects:
Primary: 62G08
Secondary: 62G15 , 62J07 , 68T05

Keywords: Confidence regions , Lasso , Regression estimation , shrinkage and thresholding methods , Statistical learning

Rights: Copyright © 2008 The Institute of Mathematical Statistics and the Bernoulli Society

JOURNAL ARTICLE
24 PAGES


SHARE
Back to Top