发表机构
Indian Statistical Institute（印度统计研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种基于狄利克雷过程先验的贝叶斯非参数回归树混合模型，利用高斯过程分裂规则统一多种树方法，实现数据驱动的集成规模选择，并证明后验收敛率，在多个基准和应用中优于现有方法。
AI 中文摘要
我们提出了一种贝叶斯非参数回归树混合模型，该模型在树-参数对上使用狄利克雷过程先验，从而能够以数据驱动的方式选择集成规模，并统一了CART、BART、随机森林和提升方法。一种由每个终端节点内高斯过程的后验预测驱动的新型分裂规则生成了灵活、平滑的决策边界；值得注意的是，高斯过程密度在GROW/PRUNE移动的Metropolis-Hastings比率中恰好抵消，确保了计算可行性。一种用于后验预测推断的精确吉布斯采样器通过随机树遍历传播不确定性。并行MPI实现将独立的树更新分配到多个处理器上，实现了足够的加速比。我们证明了在真实回归函数仅需连续性的条件下，后验分布在Hellinger距离下以$n^{-1/4}$的速率一致收敛，允许模型设定错误，这通过恒等式$h(Θ)=0$实现。在Friedman基准上的模拟显示接近名义覆盖率（高斯分布为0.94，柯西分布为0.92），对高维噪声和重尾分布具有鲁棒性，优于BART和袋装CART。在QSAR毒性、犯罪、核黄素、小麦基因组和空气质量等应用上确认了可靠的置信区间和自动稀疏性。DP混合模型为具有诚实不确定性量化的挑战性回归提供了一种原则性、鲁棒且具有理论依据的替代方案。
英文摘要
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 across processors, achieving adequate speedups. We prove posterior consistency at rate $n^{-1/4}$ in Hellinger distance under only continuity of the true regression function, allowing misspecification, via the identity $h(Θ)=0$. Simulations on Friedman benchmark show near-nominal coverage (0.94 Gaussian, 0.92 Cauchy), robust to high-dimensional noise and heavy tails, outperforming BART and bagged CART. Applications to QSAR toxicity, crime, riboflavin, wheat genomics, and air quality confirm reliable credible intervals and automatic sparsity. The DP mixture offers a principled, robust, theoretically justified alternative for challenging regression with honest uncertainty quantification.
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