敏感性分析中Shapley效应的计算
Computing Shapley Effects for Sensitivity Analysis
摘要：
Shapley效应作为一种灵敏度度量方法正受到越来越多的关注。当值函数是条件方差时，它们说明了模型输入的个体效应和高阶效应。它们在模型输入依赖下也有很好的定义。然而，与其使用相关的问题之一是计算成本。我们提出了一种新的算法，提供了重大改进的Shapley效应的计算，减少了几个数量级的计算负担（从$k!\cdot k$到$2^k$，其中$k$是输入的数量）相对于目前可用的实现。该算法在存在输入依赖性的情况下工作。该算法还可以估计相互作用的所有广义（Shapley-Owen）效应。
英文摘要：
Shapley effects are attracting increasing attention as sensitivity measures. When the value function is the conditional variance, they account for the individual and higher order effects of a model input. They are also well defined under model input dependence. However, one of the issues associated with their use is computational cost. We present a new algorithm that offers major improvements for the computation of Shapley effects, reducing computational burden by several orders of magnitude (from $k!\cdot k$ to $2^k$, where $k$ is the number of inputs) with respect to currently available implementations. The algorithm works in the presence of input dependencies. The algorithm also makes it possible to estimate all generalized (Shapley-Owen) effects for interactions.
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