Dirichlet Process Mixtures of Trees with Gaussian Process Splits: A Bayesian Nonparametric Framework with Posterior Contraction Rate

We propose a Bayesian nonparametric mixture of regression trees with a Dirichlet process prior over tree-parameter pairs, enabling data-driven selection of ensemble size and unifying CART, BART, random forests, and boosting. A novel splitting rule driven by the posterior predictive of a Gaussian pro