Dynamic Trees for Learning and Design

TL;DR

This paper introduces dynamic regression trees with particle learning algorithms for efficient online inference, enabling adaptive modeling in regression, classification, and sequential experiment design with improved performance and lower computational cost.

Contribution

It presents a novel sequential tree model with particle filtering for online learning, allowing dynamic adaptation and uncertainty quantification in regression and classification tasks.

Findings

Outperforms standard methods in nonparametric regression examples.

Effective in sequential experiment design, including active learning and optimization.

Provides a computationally efficient approach for online inference with dynamic trees.

Abstract

Dynamic regression trees are an attractive option for automatic regression and classification with complicated response surfaces in on-line application settings. We create a sequential 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. The model also facilitates a natural division of labor in our sequential particle-based inference: tree dynamics are defined through a few potential changes that are local to each newly arrived observation, while global uncertainty is captured by the ensemble of particles. 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. We detail implementation guidelines and problem specific methodology for each of these motivating applications. Throughout, it is demonstrated that our practical approach is able to provide better results compared to commonly used methods at a fraction of the cost.