Automatic Induction of Piecewise Linear Models with Decision Trees

摘要

The expressive capacity of a CART decision tree is extended by associating a linear predictor to each of the terminal nodes of the tree. The prediction is made by means of a piecewise linear model (PLM), which is more flexible than the usual piecewise constant models produced by standard regression trees. The complexity of the linear predictors at the leaves is limited by using a stepwise regression procedure, which ensures that only statistically relevant attributes are included in the regression. The accuracy and robustness of the PLM regression trees are demonstrated in a series of examples, including problems with noisy data and/or irrelevant attributes.