发表机构
Yonsei University（延世大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
RoBART通过为每棵树分配旋转，使BART能高效逼近轴不对齐的边界，并在理论上证明其适应内在维度而轴对齐BART不能。
AI 中文摘要
贝叶斯加性回归树（BART）在逼近与预测变量轴不对齐的边界时可能需要大量分裂。RoBART为每棵树分配一个由所有内部节点共享的旋转，从而在旋转后的坐标中保留轴对齐分裂和常数叶节点。我们联合提出通过Metropolis-Hastings算法在所得网格上生成Givens旋转序列和切点，并建立了相对于积分掉叶均值的条件后验的可逆性。对于具有分量特定旋转和各向异性Hölder光滑性的加性函数，我们证明了在经验$L_2$距离和噪声标准差下的后验收缩。在所述先验、设计和网格条件下，当预测变量、树和分量的数量固定且分量数不超过树数时，收缩率为由光滑性和所用旋转坐标数量决定的分量级收缩率之和。我们还建立了一个后验收缩下界，表明存在某些函数，RoBART能适应其内在维度，而轴对齐的BART则不能。
英文摘要
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.
