Cost-complexity tree pruning ($R_{\alpha }(T)=R(T)+\alpha |\mathcal{L}(T)|$)

Pruning balances a tree's empirical loss $R(T)$ against the number of leaves. Increasing $\alpha$ favors a nested sequence of smaller subtrees, obtained by removing splits with the smallest effective cost per removed leaf. Choose complexity using cross-validation or a validation set, and assess the selected tree on a separate test set. The loss can be deviance or misclassification loss; the chosen convention must be specified.