Model Tree

A Model Tree is a prediction tree that has functional models in the leaves instead of constants.

• AKA: Functional Trees, Linear Regression Trees, Piecewise Linear Model.
• Context:
  • It can produced by a Model Tree Learning System which implements a Model Tree Learning Algorithm to solve a Model Tree Learning Task.
• Example(s):
  • …
• Counter-Example(s):
  • Regression Trees.
  • Classification Trees.
  • Decision Trees.
  • Random Forests.
• See: Regression Task; Supervised Learning; Training Sample.

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References

2017a

• (Furnkranz, 2017) ⇒ Johannes Fürnkranz, (2017). "Decision Tree". In Encyclopedia of Machine Learning and Data Mining pp 330-335.
  • QUOTE: Decision trees are also often used as components in Ensemble Methods such as random forests (Breiman 2001 ) or AdaBoost (Freund and Schapire 1996). They can also be modified for predicting numerical target variables, in which case they are known as regression trees. One can also put more complex prediction models into the leaves of a tree, resulting in Model Trees.

2017b

• (Torgo, 2017) ⇒ Luı́s Torgo, (2017). "Model Trees". In Encyclopedia of Machine Learning and Data Mining pp 845-848.
  • QUOTE: 1: 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 [math]\displaystyle{ Y }[/math] and of a vector of p predictor variables, [math]\displaystyle{ \mathbf{x}= X_1, \cdots, X_p }[/math] . Model trees provide an approximation of an unknown regression function [math]\displaystyle{ Y=f(\mathbf{x})+\epsilon }[/math] with [math]\displaystyle{ Y \in \mathcal{R} }[/math] and [math]\displaystyle{ \epsilon \approx N (0, \sigma^2) }[/math]. The leaves of these trees usually contain linear regression models, although some works also consider other types of models.
  • QUOTE: 2: Model trees are motivated by the purpose of overcoming some of the known limitations of regression trees caused by their piecewise constant approximation. In effect, by using constants at the leaves, regression trees provide a coarse grained function approximation leading to poor accuracy in some domains. Model trees try to overcome this by using more complex models on the leaves.

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