具有最优决策树的非参数变量筛选
Nonparametric Variable Screening with Optimal Decision Stumps
摘要：
决策树及其集成具有丰富的诊断工具集，用于在预测模型中对变量进行排名和筛选。尽管基于树的变量重要性度量方法得到了广泛的应用，但确定它们的理论性质一直是一个挑战，因此在很大程度上尚未探索。为了解决理论和实践之间的差距，我们得出有限样本的性能保证变量选择非参数模型使用单级CART决策树（决策树桩）。在变量筛选文献中的标准操作假设下，我们发现每个变量和环境维度的边际信号强度可以分别比最先进的非参数变量选择方法弱得多和高得多。此外，与试图通过截断基扩展直接估计每个边缘投影的先前边缘筛选方法不同，这里使用的拟合模型是一个简单的、简约的决策树桩，从而消除了调整基项数量的需要。因此，令人惊讶的是，即使决策树对于估计目的是高度不准确的，它们仍然可以用于执行一致的模型选择。
英文摘要：
Decision trees and their ensembles are endowed with a rich set of diagnostic tools for ranking and screening variables in a predictive model. Despite the widespread use of tree based variable importance measures, pinning down their theoretical properties has been challenging and therefore largely unexplored. To address this gap between theory and practice, we derive finite sample performance guarantees for variable selection in nonparametric models using a single-level CART decision tree (a decision stump). Under standard operating assumptions in variable screening literature, we find that the marginal signal strength of each variable and ambient dimensionality can be considerably weaker and higher, respectively, than state-of-the-art nonparametric variable selection methods. Furthermore, unlike previous marginal screening methods that attempt to directly estimate each marginal projection via a truncated basis expansion, the fitted model used here is a simple, parsimonious decision stump, thereby eliminating the need for tuning the number of basis terms. Thus, surprisingly, even though decision stumps are highly inaccurate for estimation purposes, they can still be used to perform consistent model selection.
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