ABSTRACT While statistical learning methods have proved powerful tools for predictive modeling, the black-box nature of the models they produce can severely limit their interpretability and the ability to conduct formal inference. However, the natural structure of ensemble learners like bagged trees and random forests has been shown to admit desirable asymptotic properties when base learners are built with proper subsamples. In this work, we demonstrate that by defining an appropriate grid structure on the covariate space, we may carry out formal hypothesis tests for both variable importance and underlying additive model structure. To our knowledge, these tests represent the first statistical tools for investigating the underlying regression structure in a context such as random forests. We develop notions of total and partial additivity and further demonstrate that testing can be carried out at no additional computational cost by estimating the variance within the process of constructing the ensemble. Furthermore, we propose a novel extension of these testing procedures using random projections to allow for computationally efficient testing procedures that retain high power even when the grid size is much larger than that of the training set.

中文翻译：

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随机森林中加性结构的形式假设检验

摘要 虽然统计学习方法已被证明是预测建模的强大工具，但它们生成的模型的黑盒性质会严重限制其可解释性和进行形式推理的能力。然而，当使用适当的子样本构建基学习器时，集成学习器（如袋装树和随机森林）的自然结构已被证明具有理想的渐近特性。在这项工作中，我们证明了通过在协变量空间上定义适当的网格结构，我们可以对变量重要性和潜在的可加性模型结构进行形式化假设检验。据我们所知，这些测试代表了在随机森林等环境中调查潜在回归结构的第一个统计工具。我们开发了总可加性和部分可加性的概念，并通过估计构建集成过程中的方差，进一步证明可以在不增加计算成本的情况下进行测试。此外，我们建议使用随机投影对这些测试程序进行新的扩展，以允许计算高效的测试程序，即使在网格大小远大于训练集的情况下也能保持高功率。