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.

Challenges learning from imbalanced data using tree-based models: Prevalence estimates systematically depend on hyperparameters and can be upwardly biased

Imbalanced binary classification problems arise in many fields of study. When using machine learning models for these problems, it is common to subsample the majority class (i.e., undersampling) to create a (more) balanced dataset for model training. This biases the model's predictions because the model learns from a dataset that does not follow the same data generating process as new data. One way of accounting for this bias is to analytically map the resulting predictions to new values based on the sampling rate for the majority class, which was used to create the training dataset. While this approach may work well for some machine learning models, we have found that calibrating a random forest this way has unintended negative consequences, including prevalence estimates that can be upwardly biased. These prevalence estimates depend on both i) the number of predictors considered at each split in the random forest; and ii) the sampling rate used. We explain the former using known properties of random forests and analytical calibration. However, in investigating the latter issue, we made a surprising discovery - contrary to the widespread belief that decision trees are biased towards the majority class, they actually can be biased towards the minority class.

Using Platt's scaling for calibration after undersampling -- limitations and how to address them

When modelling data where the response is dichotomous and highly imbalanced, response-based sampling where a subset of the majority class is retained (i.e., undersampling) is often used to create more balanced training datasets prior to modelling. However, the models fit to this undersampled data, which we refer to as base models, generate predictions that are severely biased. There are several calibration methods that can be used to combat this bias, one of which is Platt's scaling. Here, a logistic regression model is used to model the relationship between the base model's original predictions and the response. Despite its popularity for calibrating models after undersampling, Platt's scaling was not designed for this purpose. Our work presents what we believe is the first detailed study focused on the validity of using Platt's scaling to calibrate models after undersampling. We show analytically, as well as via a simulation study and a case study, that Platt's scaling should not be used for calibration after undersampling without critical thought. If Platt's scaling would have been able to successfully calibrate the base model had it been trained on the entire dataset (i.e., without undersampling), then Platt's scaling might be appropriate for calibration after undersampling. If this is not the case, we recommend a modified version of Platt's scaling that fits a logistic generalized additive model to the logit of the base model's predictions, as it is both theoretically motivated and performed well across the settings considered in our study.