Semilinear regression trees

Tree-based methods refer to a class of predictive models largely employed in many scientific areas. Regression trees partition the variable space into a set of hyper-rectangles, and perform a prediction within each of them. Regression trees are conceptually simple, apparently easy to interpret and capable of dealing with non linearities and interactions. We propose a class of models here called semilinear regression tree, combining a linear component and a tree. These models can handle linear and non linear dependencies and maintains a good predictive performance, while ensuring a simple and intuitive interpretation in a generative model sense. Moreover, we propose an estimation procedure based on evolutionary algorithms.