Super greedy trees

We introduce Super Greedy Trees (SGTs), a decision-tree framework that extends CART by constructing tree splits from lasso-penalized parametric models. At each tree node, a model fitted to the local data induces an adaptive multivariate geometric cut (linear or curved) selected to greedily reduce empirical risk. This yields richer partitions than axis-parallel CART while keeping each split easy to inspect through sparse local structure. In simulated and real-world regression studies, SGTs and an ensemble extension (Super Greedy Forests, SGFs) perform well relative to CART, oblique trees, random forests, and gradient boosted trees, especially when the underlying response surface is complex. In a treadmill ECG and clinical-data case study, SGFs identify sparse combinations of signals associated with long-term survival. The SGT framework thus provides a flexible and theoretically sound approach to tree-based learning.