Global Sensitivity Analysis via Optimal Transport
利用最优传输理论构建多变量响应的重要性度量，满足输入依赖、独立性为零、函数依赖最大等性质，并应用于组装订单模拟器，揭示利润与库存不确定性驱动因素的差异。
We examine the construction of variable importance measures for multivariate responses using the theory of optimal transport. We start with the classical optimal transport formulation. We show that the resulting sensitivity indices are well-defined under input dependence, are equal to zero under statistical independence, and are maximal under fully functional dependence. Also, they satisfy a continuity property for information refinements. We show that the new indices encompass Wagner’s variance-based sensitivity measures. Moreover, they provide deeper insights into the effect of an input’s uncertainty, quantifying its impact on the output mean, variance, and higher-order moments. We then consider the entropic formulation of the optimal transport problem and show that the resulting global sensitivity measures satisfy the same properties, with the exception that, under statistical independence, they are minimal, but not necessarily equal to zero. We prove the consistency of a given-data estimation strategy and test the feasibility of algorithmic implementations based on alternative optimal transport solvers. Application to the assemble-to-order simulator reveals a significant difference in the key drivers of uncertainty between the case in which the quantity of interest is profit (univariate) or inventory (multivariate). The new importance measures contribute to meeting the increasing demand for methods that make black-box models more transparent to analysts and decision makers. This paper was accepted by Baris Ata, stochastic models and simulation. Funding: A. Figalli acknowledges the support of the ERC [Grant 721675] “Regularity and Stability in Partial Differential Equations (RSPDE)” and of the Lagrange Mathematics and Computation Research Center. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.01796 .