Sequential Regression Trees for Learning and Design

Sequential regression trees are an attractive option for automatic regression and classification with complicated response surfaces in on-line application settings. We create a dynamic tree model whose state changes in time with the accumulation of new data, and provide particle learning algorithms that allow for the efficient on-line posterior filtering of tree-states. A major advantage of tree regression is that it allows for the use of very simple models within each partition. We consider both constant and linear mean functions at the tree leaves, along with multinomial leaves for classification problems, and propose default prior specifications that allow for prediction to be integrated over all model parameters conditional on a given tree. Inference is illustrated in some standard nonparametric regression examples, as well as in the setting of sequential experiment design, including both active learning and optimization applications, and in on-line classification. Throughout, we demonstrate that the proposed algorithms are able to provide better results compared to commonly used methods at a fraction of the cost.