Splitting matters: how monotone transformation of predictor variables may improve the predictions of decision tree models
This provides guidelines for developers and users of decision tree models, including bagging and random forest, to improve prediction accuracy, though it is incremental as it refines existing methods rather than introducing a new paradigm.
The study tackled the problem that decision tree predictions are not invariant under monotone transformations of predictors when predicting unseen values near split points, showing that misclassification error can reach 9% with few observations and shrink to 1% with more. It found that using the mid-point between the two closest points for split point interpolation and applying a quantile transformation can reduce interpolation error by up to half on average.
It is widely believed that the prediction accuracy of decision tree models is invariant under any strictly monotone transformation of the individual predictor variables. However, this statement may be false when predicting new observations with values that were not seen in the training-set and are close to the location of the split point of a tree rule. The sensitivity of the prediction error to the split point interpolation is high when the split point of the tree is estimated based on very few observations, reaching 9% misclassification error when only 10 observations are used for constructing a split, and shrinking to 1% when relying on 100 observations. This study compares the performance of alternative methods for split point interpolation and concludes that the best choice is taking the mid-point between the two closest points to the split point of the tree. Furthermore, if the (continuous) distribution of the predictor variable is known, then using its probability integral for transforming the variable ("quantile transformation") will reduce the model's interpolation error by up to about a half on average. Accordingly, this study provides guidelines for both developers and users of decision tree models (including bagging and random forest).