Title: Random Forests, Decision Trees, and Categorical Predictors: The "Absent Levels" Problem,
Abstract: One advantage of decision tree based methods like random forests is their
ability to natively handle categorical predictors without having to first
transform them (e.g., by using feature engineering techniques). However, in
this paper, we show how this capability can lead to an inherent "absent levels"
problem for decision tree based methods that has never been thoroughly
discussed, and whose consequences have never been carefully explored. This
problem occurs whenever there is an indeterminacy over how to handle an
observation that has reached a categorical split which was determined when the
observation in question's level was absent during training. Although these
incidents may appear to be innocuous, by using Leo Breiman and Adele Cutler's
random forests FORTRAN code and the randomForest R package (Liaw and Wiener,
2002) as motivating case studies, we examine how overlooking the absent levels
problem can systematically bias a model. Furthermore, by using three real data
examples, we illustrate how absent levels can dramatically alter a model's
performance in practice, and we empirically demonstrate how some simple
heuristics can be used to help mitigate the effects of the absent levels
problem until a more robust theoretical solution is found.