Random Forests, Decision Trees, and Categorical Predictors: The "Absent Levels" Problem
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One of the advantages that decision trees have over many other models is their ability to natively handle categorical predictors without having to first transform them (e.g., by using one-hot encoding). However, in this paper, we show how this capability can also lead to an inherent "absent levels" problem for decision tree based algorithms that, to the best of our knowledge, has never been thoroughly discussed, and whose consequences have never been carefully explored. This predicament occurs whenever there is indeterminacy in how to handle an observation that has reached a categorical split which was determined when the observation'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 as motivating case studies, we show how overlooking the absent levels problem can systematically bias a model. Afterwards, we discuss some heuristics that can possibly be used to help mitigate the absent levels problem and, using three real data examples taken from public repositories, we demonstrate the superior performance and reliability of these heuristics over some of the existing approaches that are currently being employed in practice due to oversights in the software implementations of decision tree based algorithms. Given how extensively these algorithms have been used, it is conceivable that a sizable number of these models have been unknowingly and seriously affected by this issue---further emphasizing the need for the development of both theory and software that accounts for the absent levels problem.
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