Towards understanding the bias in decision trees

There is a widespread and longstanding belief that machine learning models are biased towards the majority (or negative) class when learning from imbalanced data, leading them to neglect or ignore the minority (or positive) class. In this study, we show that this belief is not necessarily correct for decision trees, and that their bias can actually be in the opposite direction. Motivated by a recent simulation study that suggested that decision trees can be biased towards the minority class, our paper aims to reconcile the conflict between that study and decades of other works. First, we critically evaluate past literature on this problem, finding that failing to consider the data generating process has led to incorrect conclusions about the bias in decision trees. We then prove that, under specific conditions related to the predictors, decision trees fit to purity and trained on a dataset with only one positive case are biased towards the minority class. Finally, we demonstrate that splits in a decision tree are also biased when there is more than one positive case. Our findings have implications on the use of popular tree-based models, such as random forests.