Variable selection through CART

TL;DR

This paper introduces a theoretically validated variable selection method using CART for regression and classification, providing both an exhaustive and a practical approach with proven performance guarantees.

Contribution

It presents a novel variable selection procedure based on CART with theoretical penalty calibration and validation, including a practical alternative for high-dimensional data.

Findings

Theoretical oracle inequalities established for the proposed method.

Practical procedure shown to perform well in simulations.

Method effectively selects relevant variables in regression and classification tasks.

Abstract

This paper deals with variable selection in the regression and binary classification frameworks. It proposes an automatic and exhaustive procedure which relies on the use of the CART algorithm and on model selection via penalization. This work, of theoretical nature, aims at determining adequate penalties, i.e. penalties which allow to get oracle type inequalities justifying the performance of the proposed procedure. Since the exhaustive procedure can not be executed when the number of variables is too big, a more practical procedure is also proposed and still theoretically validated. A simulation study completes the theoretical results.