We propose two algorithms for boosting random Fourier feature models for
approximating high-dimensional functions. These methods utilize the classical
and generalized analysis of variance (ANOVA) decomposition to learn low-order
functions, where there are few interactions between the variables. Our
algorithms are able to find an index set of important input variables and
variable interactions reliably. Furthermore, we generalize already existing
random Fourier feature models to an ANOVA setting, where terms of different
order can be used. Our algorithms have the advantage of interpretability,
meaning that the influence of every input variable is known in the learned
model, even for dependent input variables. We give theoretical as well as
numerical results that our algorithms perform well for sensitivity analysis.
The ANOVA-boosting step reduces the approximation error of existing methods
significantly.

提出了两种算法，用于提升随机傅里叶特征模型以近似高维函数，这些方法利用经典的方差分析和广义方差分析（ANOVA）分解学习低阶函数，其中变量之间的相互作用较少。算法能够可靠地找到重要的输入变量和变量交互的索引集，还将已有的随机傅里叶特征模型推广到 ANOVA 设置，可以使用不同阶数的项。算法具有解释性的优势，即可以了解到学习模型中每个输入变量的影响，甚至对于相关的输入变量。我们提供了理论和数值结果，证明了算法在敏感性分析方面的良好性能。ANOVA 增强步骤大大降低了现有方法的逼近误差。

ANOVA-boosting for 随机傅里叶特征

ANOVA-boosting for Random Fourier Features

Tree ensembles such as random forests and boosted trees are accurate but
difficult to understand, debug and deploy. In this work, we provide the inTrees
(interpretable trees) framework that extracts, measures, prunes and selects
rules from a tree ensemble, and calculates frequent variable interactions. An
rule-based learner, referred to as the simplified tree ensemble learner (STEL),
can also be formed and used for future prediction. The inTrees framework can
applied to both classification and regression problems, and is applicable to
many types of tree ensembles, e.g., random forests, regularized random forests,
and boosted trees. We implemented the inTrees algorithms in the "inTrees" R
package.

本文提供 inTrees 框架，通过提取、衡量、修剪和选择树集合中的规则，并计算频繁的变量交互来提高树集合的可解释性。inTrees 框架可以应用于分类和回归问题，并适用于多种树集合类型，例如随机森林、正则化随机森林和 Boosted Trees。