{salary }and {height table example data with three variables (ageheightand salaryid age height salary the {salary surrogate rule completely mimics the primary rulein the sense that the data splits induced by these rules are identical namelyboth rules partition the data into two sets (by id{ and { on the other handthe {height rule is less similar to the primary rulesince it causes the different partition { and { it is up to the user to define the number of surrogate rules for each tree node as soon as these surrogate rules are availablewe can use them to handle new data pointeven if the main rule cannot be applied due to missing value of the primary variable jspecificallyif the observation is missing the primary split variablewe apply the first (bestsurrogate rule if the first surrogate variable is also missingwe apply the second best surrogate ruleand so on controlling the tree shape eventuallywe are interested in getting the right-size tree namelya tree that shows good generalization properties it was already discussed in section (figure that shallow trees tend to underfit and deep trees tend to overfit the data basicallya shallow tree does not produce sufficient number of splits and deep tree will produce many partitions and thus many leaf nodes if we grow the tree to sufficient deptheach training sample will occupy separate leaf and we will observe zero loss with respect to the training data the above phenomenon is illustrated in figure which presents the cross-validation loss and the training loss as function of the tree depth in order to overcome the underand the overfitting problembreiman et al [ examined the possibility of stopping the tree from growing as soon as the decrease in loss due to split of node vas expressed in the difference of ( and ( )is smaller than some predefined parameter under this settingthe tree construction process will terminate when no leaf node can be split such that the contribution to the training loss after this split is greater than the authors found that this approach was unsatisfactory specificallyit was noted that very small leads to an excessive amount of splitting and thus causes overfitting increasing did not work either the problem is that the nature of the proposed rule is one-step-lookahead to see thisconsider tree node for which the best possible decrease in loss is