Binary Split Categorical feature with Mean Absolute Error Criteria in CART

In the context of the Classification and Regression Trees (CART) algorithm, the efficient splitting of categorical features using standard criteria like GINI and Entropy is well-established. However, using the Mean Absolute Error (MAE) criterion for categorical features has traditionally relied on various numerical encoding methods. This paper demonstrates that unsupervised numerical encoding methods are not viable for the MAE criteria. Furthermore, we present a novel and efficient splitting algorithm that addresses the challenges of handling categorical features with the MAE criterion. Our findings underscore the limitations of existing approaches and offer a promising solution to enhance the handling of categorical data in CART algorithms.