从观测数据学习全局灵敏度指标：一种基于元模型的方法

中文摘要 AI 辅助

经典的基于方差的全局灵敏度分析（GSA）假设输入-输出机制可以在设计好的采样方案下重复评估，但当仅有给定的观测样本可用时，这一假设不可行。我们提出MM-GSA，一种基于元模型的从观测数据中进行GSA的方法，其中监督学习近似系统性的输入-输出关系。MM-GSA结合了关于输入相关性的两个互补视角：一个是一阶Sobol'指数的模型无关估计量，量化输入对系统性响应变异的贡献；另一个是新的基于触发器的结构指数，量化预测性能如何依赖于不同预测子集上预测变量的可用性。我们在输入独立性下为两个估计量建立了相合性，并为结构指数建立了变量选择性质。蒙特卡洛实验和NHANES应用展示了它们的有限样本行为，并表明这两种度量提供了关于输入相关性的互补信息。

英文摘要

Classical variance-based Global Sensitivity Analysis (GSA) assumes that the input--output mechanism can be repeatedly evaluated under a designed sampling scheme, which is infeasible when only a given sample of observations is available. We propose MM--GSA, a metamodel-based approach to GSA from observational data, in which supervised learning approximates the systematic input--output relationship. MM--GSA combines two complementary perspectives on input relevance: a model-agnostic estimator of the first-order Sobol' index, quantifying the contribution of an input to the variability of the systematic response, and a new trigger-based structural index, quantifying how predictive performance depends on the availability of a predictor across alternative predictor subsets. We establish consistency for both estimators and a variable-selection property for the structural index under input independence. Monte Carlo experiments and an NHANES application illustrate their finite-sample behavior and show that the two measures provide complementary information on input relevance.

发表机构

• University of Naples Federico II（那不勒斯费德里科二世大学）
• Polytechnic and Basic Sciences School（理工与基础科学学院）
• Department of Electrical Engineering and Information Technology（电气与信息工程系）

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