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

arXiv: https://arxiv.org/abs/2609.40342 · HTML: https://mlsanity.com/paper/2609.40342/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 31 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Builds on (most cited first, 2 of 2)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Consistency of random forests](https://mlsanity.com/paper/1405.2881/) (2014)

## Abstract (arXiv)

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.