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 process within each terminal node generates flexible, smooth decision boundaries; remarkably, the GP density cancels exactly in the Metropolis--Hastings ratio for GROW/PRUNE moves, ensuring computational feasibility. An exact Gibbs sampler for posterior predictive inference propagates uncertainty through random tree traversal. A parallel MPI implementation distributes independent tree updates acro...
| Authors | Subhasish Basak, Anik Roy, Sourabh Bhattacharya |
|---|---|
| Primary category | stat.ME |
| Published | 22 August 2026 |
| Last updated at source | 22 August 2026 |
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