On sparse optimal regression trees

In this paper, we model an optimal regression tree through a continuous optimization problem, where compromise between prediction accuracy and both types of sparsity, namely local global, is sought. Our approach can accommodate important desirable properties for the task, such as cost-sensitivity fairness. Thanks to smoothness predictions, derive explanations on predictor variables. The computational experience reported shows outperformance our in terms against standard benchmark methods CART, OLS LASSO. Moreover, scalability with respect size training sample illustrated.