Challenges in the calibration of tree-based models for imbalanced classification

When using machine learning for imbalanced binary classification problems, it is common to subsample the majority class to create a (more) balanced training dataset. This biases the model's predictions because the model learns from data that is not fully representative of the underlying population of interest. One way of accounting for this bias is analytically mapping the resulting predictions to new values based on the sampling rate for the majority class. We show that calibrating a random forest this way has negative consequences, including prevalence estimates that depend on both the number of predictors considered at each split in the random forest and the sampling rate used. We explain the former using known properties of random forests and analytical calibration and the latter by demonstrating a bias in decision trees. In contradiction with much of the existing literature, we show that decision trees can be biased towards the minority class. These issues indicate that tree-based models trained on undersampled data should not be calibrated analytically. Calibration approaches that can learn a miscalibration pattern in the original model (e.g., beta calibration) are more suitable.