The ortho tree model. A very interpretable regression tree with flexible ortho leaves

In this paper we consider the problem of nonparametric function estimation of high dimensional data. The proposed methodology follows the general idea behind Model Trees, integrating the partition strategy of regression trees with Generalized Additive Models. Specifically, we use the Ortho model, formed by the sum of univariate piecewise linear functions, fitted with the orthogonal projections of the input data. The model is fully interpretable and visualizable, and we provide a means for graphical representation of the obtained structure, allowing an easy understanding of the role of each input in modeling the output. The model performance is assessed on a set of synthetic test problems, and compared with other regression methods regarding accuracy and interpretability properties.