An evolutionary estimation procedure for generalized semilinear regression trees

In many applications, the presence of interactions or even mild non-linearities can affect inference and predictions. For that reason, we suggest the use of a class of models laying between statistics and machine learning and we propose a learning procedure. The models combine a linear part and a tree component that is selected via an evolutionary algorithm, and they can be adopted for any kinds of response, such as, for instance, continuous, categorical, ordinal responses, and survival times. They are inherently interpretable but more flexible than standard regression models, as they easily capture non-linear and interaction effects. The proposed genetic-like learning algorithm allows avoiding a greedy search of the tree component. In a simulation study, we show that the proposed approach has a performance comparable with other machine learning algorithms, with a substantial gain in interpretability and transparency, and we illustrate the method on a real data set.