On Semi-parametric Inference for BART
On Semi-parametric Inference for BART
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BART 的半参数推理
DOI：
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发表时间：
2020
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通讯作者：
V. Ročková
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作者：
V. Ročková
人们越来越认识到贝叶斯机器学习作为一个平台的潜力，它可以提供灵活的建模，准确的预测以及连贯的不确定性陈述。特别是，贝叶斯加性回归树（BART）已经成为当今最有效的通用方法之一，在最小假设下进行预测建模。机器学习的统计理论发展主要涉及在恢复有限维对象（曲线或密度）时的近似性或估计率。尽管有一系列令人印象深刻的理论结果，但文献对不确定性的量化基本上保持沉默。在这项工作中，我们继续了BART最近发起的理论研究（Ro Rickkov 'a和货车der Pas，2017）。我们专注于统计推断问题。特别是，我们研究了Bernstein-von Mises（BvM）现象（即渐近正态性）的平滑线性泛函的回归表面的框架内的非参数回归固定协变量。我们的半参数BVM结果表明，除了率最优估计，BART也可以用于有效的统计推断。
There has been a growing realization of the potential of Bayesian machine learning as a platform that can provide both flexible modeling, accurate predictions as well as coherent uncertainty statements. In particular, Bayesian Additive Regression Trees (BART) have emerged as one of today’s most effective general approaches to predictive modeling under minimal assumptions. Statistical theoretical developments for machine learning have been mostly concerned with approx-imability or rates of estimation when recovering infinite dimensional objects (curves or densities). Despite the impressive array of available theoretical results, the literature has been largely silent about uncertainty quantification. In this work, we continue the theoretical investigation of BART initiated recently by (Ro ˇ ckov ´ a and van der Pas, 2017). We focus on statistical inference questions. In particular, we study the Bernstein-von Mises (BvM) phenomenon (i.e. asymptotic normality) for smooth linear functionals of the regression surface within the framework of non-parametric regression with fixed covariates. Our semi-parametric BvM results show that, beyond rate-optimal estimation, BART can be also used for valid statistical inference.