Shapley效应在具有相关输入的可靠性导向敏感性分析中的发展与应用
Developments and applications of Shapley effects to reliability-oriented sensitivity analysis with correlated inputs
AI总结：
本文提出基于Shapley值的“目标Shapley效应”新敏感性指数，用于在相关输入条件下度量输入对关键失效事件的影响，并给出两种估计算法及实际应用验证。
摘要：
可靠性导向的敏感性分析方法已被开发用于理解模型输入相对于表征系统失效事件（例如，模型输出超过阈值）的影响。在该领域中，目标敏感性分析主要侧重于捕捉输入对此类关键事件发生的影响。本文提出了新的目标敏感性指数，这些指数基于Shapley值，被称为“目标Shapley效应”，能够在输入相关的条件下提供可解释的敏感性度量。本文提出了两种算法（一种基于蒙特卡洛采样，另一种是基于最近邻过程的给定数据算法），用于基于$\ell^2$范数估计这些目标Shapley效应。此外，通过各种玩具案例对这些目标Shapley效应的行为进行了理论和实证研究。最后，讨论了这些新指数在两个实际用例（一个河流洪水模型和一个COVID-19流行病学模型）中的应用。
英文摘要：
Reliability-oriented sensitivity analysis methods have been developed for understanding the influence of model inputs relative to events which characterize the failure of a system (e.g., a threshold exceedance of the model output). In this field, the target sensitivity analysis focuses primarily on capturing the influence of the inputs on the occurrence of such a critical event. This paper proposes new target sensitivity indices, based on the Shapley values and called "target Shapley effects", allowing for interpretable sensitivity measures under dependent inputs. Two algorithms (one based on Monte Carlo sampling, and a given-data algorithm based on a nearest-neighbors procedure) are proposed for the estimation of these target Shapley effects based on the $\ell^2$ norm. Additionally, the behavior of these target Shapley effects are theoretically and empirically studied through various toy-cases. Finally, the application of these new indices in two real-world use-cases (a river flood model and a COVID-19 epidemiological model) is discussed.
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