Unbiased recursive partitioning: A conditional inference framework
Unbiased recursive partitioning: A conditional inference framework
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DOI：
10.1198/106186006x133933
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发表时间：
2006-09-01
影响因子：
2.4
通讯作者：
Zeileis, Achim
中科院分区：
文献类型：
--
作者：
Hothorn, Torsten;Hornik, Kurt;Zeileis, Achim
递归二进制划分是一种流行的回归分析工具。通常用于拟合这类模型的穷举搜索法的两个基本问题早已为人所知：过度拟合和对协变量的选择偏向，可能存在许多分裂或缺失值。虽然剪枝过程能够解决过拟合问题，但变量选择偏差仍然严重影响树结构回归模型的解释能力。对于一些特殊情况，有人建议不偏不倚的程序，但缺乏共同的理论基础。我们提出了一个用于递归划分的统一框架，该框架将树结构回归模型嵌入到定义良好的条件推理过程理论中。实现了基于多个测试过程的停止准则，结果表明，结果树的预测性能与已建立的穷举搜索过程的性能一样好。事实证明，这两种方法的划分以及由此产生的模型在结构上是不同的，证实了无偏变量选择的必要性。此外，还证明了早停树的预测精度与变量选择无偏的修剪树的预测精度是等价的。本文提出的方法适用于所有类型的回归问题，包括名义的、顺序的、数值的、删失的以及多变量的响应变量和协变量的任意测量尺度。来自青光眼分类、结节阳性乳腺癌生存率和乳房X光检查经验的研究数据被重新分析。
Recursive binary partitioning is a popular tool for regression analysis. Two fundamental problems of exhaustive search procedures usually applied to fit such models have been known for a long time: overfitting and a selection bias towards covariates with many possible splits or missing values. While pruning procedures are able to solve the over-fitting problem, the variable selection bias still seriously affects the interpretability of tree-structured regression models. For some special cases unbiased procedures have been suggested, however lacking a common theoretical foundation. We propose a unified framework for recursive partitioning which embeds tree-structured regression models into a well defined theory of conditional inference procedures. Stopping criteria based on multiple test procedures are implemented and it is shown that the predictive performance of the resulting trees is as good as the performance of established exhaustive search procedures. It turns out that the partitions and therefore the models induced by both approaches are structurally different, confirming the need for an unbiased variable selection. Moreover, it is shown that the prediction accuracy of trees with early stopping is equivalent to the prediction accuracy of pruned trees with unbiased variable selection. The methodology presented here is applicable to all kinds of regression problems, including nominal, ordinal, numeric, censored as well as multivariate response variables and arbitrary measurement scales of the covariates. Data from studies on glaucoma classification, node positive breast cancer survival and mammography experience are re-analyzed.