Monotone Shrinkage of Trees

Abstract

We investigate a new method for regression trees which obtains estimates and predictions subject to constraints on the coefficients representing the effects of splits in the tree. The procedure leads to both shrinking of the node estimates and pruning of branches in the tree and for some problems gives better predictions than cost-complexity pruning used in the classification and regression tree (CART) algorithm. The new method is based on the least absolute shrinkage and selection operator (LASSO) method developed by Tibshirani.

Key Words:

• CART
• Classification and regression trees
• LASSO