LASSO, Iterative Feature Selection and the Correlation Selector: Oracle Inequalities and Numerical Performances

Details LASSO, Iterative Feature Selection and the Correlation Selector: Oracle Inequalities and Numerical Performances LASSO, Iterative Feature Selection and the Correlation Selector: Oracle Inequalities and Numerical Performances

2007-10-24

arxiv.org/abs/0710.4466v4

Electronic Journal of Statistics 2 (2008) pp. 1129-1152

Mathematics

Statistics Theory

Scientific paper

10.1214/08-EJS299

We propose a general family of algorithms for regression estimation with quadratic loss. Our algorithms are able to select relevant functions into a large dictionary. We prove that a lot of algorithms that have already been studied for this task (LASSO and Group 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.

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