On the Computational Efficiency of Bayesian Additive Regression Trees: An Asymptotic Analysis
贝叶斯加性回归树的计算效率：渐近分析AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要核心是通用 BART 采样器的计算渐近理论，仅提及因果用途，不足以归入所列具体领域。
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贝叶斯加性回归树的计算效率：渐近分析
- 研究问题
- 训练样本增加时，BART 采样器到达高后验密度区域的时间如何变化，多峰后验是否造成计算困难，哪些调整可能缓解？
- 方法与思路
- 作者对离散协变量下稍作修改的默认采样器开展渐近命中时间分析，并以默认采样器模拟检查树数量、温度及其他设置的影响。
- 材料陈述的贡献
- 摘要称后验多峰性使命中时间随样本量增加，而增加树数量或提高采样温度可缓和该趋势，模拟对默认采样器也观察到类似现象。
- 阅读关注点
- 应核对修改版本与默认采样器的区别、高后验密度集合和命中时间定义，以及增加树数或温度对计算成本与目标后验的影响。
- 阅读边界
- 所据为 arXiv 预印本，同行评审及期刊接收未核实；理论针对离散协变量和修改采样器，摘要未说明能否推广至其他数据及实现。
原文摘要
Bayesian Additive Regression Trees (BART) is a popular Bayesian non-parametric regression model that is commonly used in causal inference and beyond. Its strong predictive performance is supported by well-developed estimation theory, comprising guarantees that its posterior distribution concentrates around the true regression function at optimal rates under various data generative settings and for appropriate prior choices. However, the computational properties of the widely-used BART sampler proposed by Chipman et al. (2010) are yet to be well-understood. In this paper, we perform an asymptotic analysis of a slightly modified version of the default BART sampler when fitted to data-generating processes with discrete covariates. We show that the sampler's time to convergence, evaluated in terms of the hitting time of a high posterior density set, increases with the number of training samples, due to the multi-modal nature of the target posterior. On the other hand, we show that this trend can be dampened by simple changes, such as increasing the number of trees in the ensemble or raising the temperature of the sampler. These results provide a nuanced picture on the computational efficiency of the BART sampler in the presence of large amounts of training data while suggesting strategies to improve the sampler. We complement our theoretical analysis with a simulation study focusing on the default BART sampler. We observe that the increasing trend of convergence time against number training samples holds for the default BART sampler and is robust to changes in sampler initialization, number of burn-in iterations, feature selection prior, and discretization strategy. On the other hand, increasing the number of trees or raising the temperature sharply dampens this trend, as indicated by our theory.