Top-down induction of model trees with regression and splitting nodes.

Abstract

Model trees are an extension of regression trees that associate leaves with multiple regression models. In this paper, a method for the data-driven construction of model trees is presented, namely, the Stepwise Model Tree Induction (SMOTI) method. Its main characteristic is the induction of trees with two types of nodes: regression nodes, which perform only straight-line regression, and splitting nodes, which partition the feature space. The multiple linear model associated with each leaf is then built stepwise by combining straight-line regressions reported along the path from the root to the leaf. In this way, internal regression nodes contribute to the definition of multiple models and have a "global" effect, while straight-line regressions at leaves have only "local" effects. Experimental results on artificially generated data sets show that SMOTI outperforms two model tree induction systems, M5' and RETIS, in accuracy. Results on benchmark data sets used for studies on both regression and model trees show that SMOTI performs better than RETIS in accuracy, while it is not possible to draw statistically significant conclusions on the comparison with M5'. Model trees induced by SMOTI are generally simple and easily interpretable and their analysis often reveals interesting patterns.