The HPFOREST Procedure

To predict an observation, the HPFOREST procedure first assigns the observation to a single leaf in each decision tree in the forest, then uses that leaf to make a prediction based on the tree that contains the leaf, and finally simply averages the predictions over the trees. For an interval target, the prediction in a leaf equals the average of the target values among the bagged training observations in that leaf. For a nominal target, the posterior probability of a target category equals the proportion of that category among the bagged training observations in that leaf. The predicted nominal target category is the category with the largest posterior probability. In case of a tie, the first category that occurs in the training data is the prediction.

The HPFOREST procedure also computes out-of-bag predictions. The out-of-bag prediction of an observation uses only trees for which the observation is out of bag (that is, not selected as part of the training data for that tree).

A model is worthless if its predictions are no better than predictions without a model. For an interval target, the no-model prediction of an observation is the average of the target among training observations. For a nominal target, the no-model posterior probabilities are the class proportions in the training data. The no-model predictions are the same for every observation.