Incremental learning of linear model trees

A linear model tree is a decision tree with a linear functional model in each leaf. Previous model tree induction algorithms have been batch techniques that operate on the entire training set. However there are many situations when an incremental learner is advantageous. In this article a new batch model tree learner is described with two alternative splitting rules and a stopping rule. An incremental algorithm is then developed that has many similarities with the batch version but is able to process examples one at a time. An online pruning rule is also developed. The incremental training time for an example is shown to only depend on the height of the tree induced so far, and not on the number of previous examples. The algorithms are evaluated empirically on a number of standard datasets, a simple test function and three dynamic domains ranging from a simple pendulum to a complex 13 dimensional flight simulator. The new batch algorithm is compared with the most recent batch model tree algorithms and is seen to perform favourably overall. The new incremental model tree learner compares well with an alternative online function approximator. In addition it can sometimes perform almost as well as the batch model tree algorithms, highlighting the effectiveness of the incremental implementation.