arXiv：cs.LG· Jeongung Heo, Seonghyun Jeong·· 4 小时前AI 评分34
RoBART：带树级旋转的贝叶斯加性回归树
RoBART: Bayesian Additive Regression Trees with Tree-Specific Rotations
AI 导读
RoBART 为每棵 BART 树分配一个由所有内部节点共享的旋转，在旋转坐标系中保留轴对齐分裂与常数叶节点，并用 Metropolis-Hastings 联合提议 Givens 旋转序列与切点。
正文
Abstract:Bayesian additive regression trees (BART) can require many splits to approximate boundaries misaligned with the predictor axes. RoBART assigns each tree a rotation shared by all internal nodes, retaining axis-aligned splits in rotated coordinates and constant leaves. We jointly propose a Givens rotation sequence and cutpoints on the resulting grid by Metropolis-Hastings and establish reversibility with respect to the conditional posterior with leaf means integrated out. For additive functions with component-specific rotations and anisotropic Hölder smoothness, we prove posterior contraction in empirical $L_2$ distance and for the noise standard deviation. Under the stated prior, design, and grid conditions, with fixed numbers of predictors, trees, and components and no more components than trees, the rate is a sum of componentwise rates determined by smoothness and the number of rotated coordinates used. We also establish a posterior contraction lower bound showing that there exist functions for which RoBART adapts to the intrinsic dimension but axis-aligned BART does not.
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG); Statistics Theory (math.ST) |
| Cite as: | arXiv:2610.10214 [stat.ML] |
| (or arXiv:2610.10214v1 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2610.10214 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Jeongung Heo [view email]
[v1]
Wed, 7 Oct 2026 15:12:54 UTC (290 KB)
来源：arXiv：cs.LG · arxiv.org