Monotone shrinkage of trees

We investigate a new method for regression trees which obtains estimates an d predictions subject to constraints on the coefficients representing the e ffects 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 gi ves better predictions than cost-complexity pruning used in the classificat ion and regression tree (CART) algorithm. The new method is based on the le ast absolute shrinkage and selection operator (LASSO) method developed by T ibshirani.