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Variable selection through CART∗

Published online by Cambridge University Press:  22 October 2014

Marie Sauve  and
Christine Tuleau-Malot
Marie Sauve
Affiliation:
Lycée Jules Haag, 25000 Besançon, France. m.sauve@sfr.fr
Christine Tuleau-Malot
Affiliation:
Laboratoire Jean-Alexandre Dieudonné, CNRS UMR 6621, Université de Nice Sophia-Antipolis Parc Valrose, 06108 Nice cedex 2, France; christine.malot@unice.fr
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Abstract

This paper deals with variable selection in regression and binary classificationframeworks. It proposes an automatic and exhaustive procedure which relies on the use ofthe CART algorithm and on model selection via penalization. This work, of theoreticalnature, aims at determining adequate penalties, i.e. penalties whichallow achievement of oracle type inequalities justifying the performance of the proposedprocedure. Since the exhaustive procedure cannot be realized when the number of variablesis too large, a more practical procedure is also proposed and still theoreticallyvalidated. A simulation study completes the theoretical results.

Keywords

Binary classificationCARTmodel selectionpenalizationregressionvariable selection
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 18 , 2014 , pp. 770 - 798
Copyright
© EDP Sciences, SMAI 2014

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