A new parametric information-gain criterion for tree-based machine learning algorithms

Decision Trees (DTs) remain one of the most important algorithms in machine learning for their simplicity, interpretability, and often satisfactory performance. Furthermore, they are critical foundational components for more performant models such as Random Forests (RFs) and Gradient Boosted Trees. Central to DTs is the splitting process, where data is partitioned according to criteria traditionally based on information-theoretic measures such as Shannon entropy or Gini index. In this article, we propose a novel parametric entropy-based information gain criterion designed to generalize and extend classical entropic measures to improve classification performance in DTs and RFs. We introduce a five-parameter entropy formulation capable of replicating and extending known entropy measures. This new criterion was incorporated into DT and RF classifiers and evaluated on a collection of 18 benchmarking datasets, including both synthetic and real-world data retrieved from publicly available repositories. Performance was assessed using 5-fold cross-validation and optimized via Bayesian hyperparameter search, with weighted F1-score as the primary metric. Compared to splitting criteria based on existing entropy/purity measures ( e.g ., Gini, Shannon, Rényi, and Tsallis), our method yielded statistically significant improvements in classification performance across most datasets. On multiclass and imbalanced datasets, such as the Wine Quality dataset, F1-score improvements exceeded 40% using RF algorithms. Bayesian signed-rank tests confirmed the robustness of our method, which never underperformed relative to standard approaches. The proposed entropy-based splitting criterion offers a flexible and effective alternative to classical information-theoretic measures, delivering improvements in classification performance.