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arXiv 2208.06151cs.LGmath.STstat.MLstat.TH
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通过低维结构的功能分解统一局部和全局模型解释

Unifying local and global model explanations by functional decomposition of low dimensional structures

University of Copenhagen(哥本哈根大学);Heidelberg University(海德堡大学);Leibniz Institute for Prevention Research and Epidemiology – BIPS(莱布尼茨预防研究与流行病学研究所(BIPS));University of Bremen(不来梅大学)

Munir Hiabu, Joseph T. Meyer, Marvin N. Wright

摘要:

我们考虑一个全局表示的回归或分类功能分解成任意顺序的主要和相互作用的组件的总和。我们提出了一个新的识别约束,允许提取干预SHAP值和部分依赖图,从而统一本地和全球的解释。通过我们提出的识别,特征的部分依赖图对应于主效应项加上截距。特征$k$的介入SHAP值是主分量和包括$k$的所有交互分量的加权和,权重由分量维数的倒数给出。这为当地的解释带来了新的视角,例如以前仅由博弈论驱动的SHAP值。我们表明,分解可以用来减少直接和间接的偏见,通过删除所有组件,包括一个受保护的功能。最后,我们提出了一种新的特征重要性度量方法。原则上,我们提出的功能分解可以应用于任何机器学习模型,但精确计算只适用于低维结构或这些结构的集合。我们提供了一个算法和有效的实现梯度提升树(xgboost)和随机种植的森林。进行的实验表明,我们的方法提供了有意义的解释,并揭示了更高阶的相互作用。所提出的方法在R包中实现,可在\url{https://github.com/PlantedML/glex}获得。

英文摘要:

We consider a global representation of a regression or classification function by decomposing it into the sum of main and interaction components of arbitrary order. We propose a new identification constraint that allows for the extraction of interventional SHAP values and partial dependence plots, thereby unifying local and global explanations. With our proposed identification, a feature's partial dependence plot corresponds to the main effect term plus the intercept. The interventional SHAP value of feature $k$ is a weighted sum of the main component and all interaction components that include $k$, with the weights given by the reciprocal of the component's dimension. This brings a new perspective to local explanations such as SHAP values which were previously motivated by game theory only. We show that the decomposition can be used to reduce direct and indirect bias by removing all components that include a protected feature. Lastly, we motivate a new measure of feature importance. In principle, our proposed functional decomposition can be applied to any machine learning model, but exact calculation is only feasible for low-dimensional structures or ensembles of those. We provide an algorithm and efficient implementation for gradient-boosted trees (xgboost) and random planted forest. Conducted experiments suggest that our method provides meaningful explanations and reveals interactions of higher orders. The proposed methods are implemented in an R package, available at \url{https://github.com/PlantedML/glex}.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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