Model Trees

Synonyms

Functional trees, Linear regression trees, Piecewise linear models

Definition

Model trees are supervised learning methods that obtain a type of tree-based regression model, similar to regression trees, with the particularity of having functional models in the leaves instead of constants. These methods address multiple regression problems. In these problems we are usually given a training sample of n observations of a target continuous variable Y and of a vector of p predictor variables, $\mathbf{x} = X_{1},\cdots \,,X_{p}$. Model trees provide an approximation of an unknown regression function Y = f(x) +ɛ with $Y \in \mathfrak{R}$ and $\varepsilon \approx N(0,\sigma ^{2})$. The leaves of these trees usually contain linear regression models, although some works also consider other types of models.

Motivation and Background

Model trees are motivated by the purpose of overcoming some of the known limitations of regression trees caused by their piecewise constant...