Learning Global Sensitivity Indices from Observational Data: A Metamodel-Based Approach

Özetle: 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 observati…

Özet

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.

Orijinal Özet (İngilizce)

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.

Kaynak: arXiv:2609.40342 · PDF