[论文解读] Visualizing the Effects of Predictor Variables in Black Box Supervised Learning Models

Daniel W. Apley, Jingyu Zhu|arXiv (Cornell University)|Dec 27, 2016

Data Analysis with R参考文献 13被引用 259

一句话总结

引入累积局部效应（ALE）图，用于在黑箱模型中可视化预测变量的效应，解决PD图的外推问题和M图的偏差，计算开销更低，并提供R包ALEPlot。

ABSTRACT

When fitting black box supervised learning models (e.g., complex trees, neural networks, boosted trees, random forests, nearest neighbors, local kernel-weighted methods, etc.), visualizing the main effects of the individual predictor variables and their low-order interaction effects is often important, and partial dependence (PD) plots are the most popular approach for accomplishing this. However, PD plots involve a serious pitfall if the predictor variables are far from independent, which is quite common with large observational data sets. Namely, PD plots require extrapolation of the response at predictor values that are far outside the multivariate envelope of the training data, which can render the PD plots unreliable. Although marginal plots (M plots) do not require such extrapolation, they produce substantially biased and misleading results when the predictors are dependent, analogous to the omitted variable bias in regression. We present a new visualization approach that we term accumulated local effects (ALE) plots, which inherits the desirable characteristics of PD and M plots, without inheriting their preceding shortcomings. Like M plots, ALE plots do not require extrapolation; and like PD plots, they are not biased by the omitted variable phenomenon. Moreover, ALE plots are far less computationally expensive than PD plots.

研究动机与目标

• 激励在黑箱模型中可视化主效应和低阶交互的需求。
• 识别当预测变量相互依赖或远离独立时，偏依赖（PD）和边际（M）图的局限性。
• 提出累积局部效应（ALE）图，在避免外推和偏差的同时保持计算高效。
• 提供理论属性、实用定义，以及实现路径（R包ALEPlot）。

提出的方法

• 将累积局部效应（ALE）定义为预测变量效应的可视化。
• 证明ALE图不需要超出训练数据包络的外推。
• 表明ALE图不受PD图固有的忽略变量问题的偏差。
• 将ALE图的计算成本与PD图进行比较，显示显著的效率提升。
• 在更新版本中参考 refined ALE 定义、示例和渐近性质。
• 通过ALEPlot R包提供实现细节。

实验结果

研究问题

• RQ1 ALE图是否能在不对训练数据包络外推的情况下准确反映预测变量的效应？
• RQ2 当预测变量相关时，ALE图是否避免PD图所受的忽略变量偏差？
• RQ3 在典型的黑箱模型中，ALE图是否比部分依赖（PD）图更具计算效率？
• RQ4 ALE效应与估计量的渐进性质及实际定义是什么？
• RQ5 在示例和真实数据情景中，所提方法的表现如何？

主要发现

• ALE图在不具备PD与M图的关键缺点（无外推、偏差更小）的情况下继承了它们的有利之处。
• 当预测变量相关时，ALE图不受PD图的忽略变量问题的偏差。
• ALE图在计算上远比PD图高效。
• CRAN上提供的R包ALEPlot实现这些图，更新版本中有更精炼的定义和理论属性。