arXiv Machine Learning
Sep 24

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

arXiv:2609. 27930v1 Announce Type: cross Abstract: 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.

By Subhasish Basak, Anik Roy, Sourabh Bhattacharya
arXiv Statistics ML
Oct 5

A Residual Tree Gaussian Process Modeling Framework for High-Dimensional Data

The paper introduces ResTGP, a Bayesian residual tree Gaussian Process framework designed for large, high‑dimensional spatial datasets with heterogeneous structures. It decomposes a Gaussian process across a dyadic tree, iteratively computing predictive and residual processes at each node to capture multi‑scale covariance efficiently. The method employs recursive message passing for linear‑time Bayesian inference and demonstrates posterior consistency, with numerical experiments and a storm surge application highlighting its advantages.

By Pulong Ma, Li Ma
arXiv Machine Learning
Aug 18

On Stopping Rules and Spatial Adaptation for CART

arXiv:2608. 15649v1 Announce Type: cross Abstract: The popular CART algorithm for regression trees combines a greedy splitting rule with a stopping rule, but while the splitting rule has been well studied, the statistical role of stopping rules is less well understood.

By Zineng Xu, Yuchao Cai, Yan Shuo Tan