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Global sensitivity analysis is a set of methods aiming at quantifying the contribution of an uncertain input parameter of the model (or combination of parameters) on the variability of the response. We consider here the estimation of the…

Statistics Theory · Mathematics 2020-01-22 Viet Chi Tran , Gwenaëlle Castellan , Anthony Cousien , Chi Tran

The coefficient of determination, the $R^2$, is often used to measure the variance explained by an affine combination of multiple explanatory covariates. An attribution of this explanatory contribution to each of the individual covariates…

Methodology · Statistics 2020-08-11 Daniel Fryer , Inga Strumke , Hien Nguyen

In the context of global sensitivity analysis, the Sobol' indices constitute a powerful tool for assessing the relative significance of the uncertain input parameters of a model. We herein introduce a novel approach for evaluating these…

Computation · Statistics 2016-05-31 K. Konakli , B. Sudret

Global sensitivity analysis aims at quantifying the impact of input variability onto the variation of the response of a computational model. It has been widely applied to deterministic simulators, for which a set of input parameters has a…

Computation · Statistics 2021-06-01 X. Zhu , B. Sudret

The estimation of variance-based importance measures (called Sobol' indices) of the input variables of a numerical model can require a large number of model evaluations. It turns to be unacceptable for high-dimensional model involving a…

Statistics Theory · Mathematics 2013-05-28 Matieyendou Lamboni , Bertrand Iooss , Anne-Laure Popelin , Fabrice Gamboa

Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the variability of a quantity of interest (output of…

Statistics Theory · Mathematics 2013-03-27 Alexandre Janon , Thierry Klein , Agnes Lagnoux-Renaudie , Maëlle Nodet , Clémentine Prieur

Global sensitivity analysis aims at determining which uncertain input parameters of a computational model primarily drives the variance of the output quantities of interest. Sobol' indices are now routinely applied in this context when the…

Computation · Statistics 2017-05-30 R. Schöbi , B. Sudret

Data samples collected for training machine learning models are typically assumed to be independent and identically distributed (iid). Recent research has demonstrated that this assumption can be problematic as it simplifies the manifold of…

Machine Learning · Computer Science 2019-10-16 Kaixuan Zhang , Qinglong Wang , Xue Liu , C. Lee Giles

Probabilistic graphical models, such as Markov random fields (MRF), exploit dependencies among random variables to model a rich family of joint probability distributions. Sophisticated inference algorithms, such as belief propagation (BP),…

Social and Information Networks · Computer Science 2020-04-22 Yifei Liu , Chao Chen , Xi Zhang , Sihong Xie

In this paper, we consider a regression model built on dependent variables. This regression modelizes an input output relationship. Under boundedness assumptions on the joint distribution function of the input variables, we show that a…

Statistics Theory · Mathematics 2012-03-14 Gaëlle Chastaing , Fabrice Gamboa , Clémentine Prieur

Variable selection or importance measurement of input variables to a machine learning model has become the focus of much research. It is no longer enough to have a good model, one also must explain its decisions. This is why there are so…

Machine Learning · Computer Science 2023-08-01 Vincent Lemaire , Fabrice Clérot , Marc Boullé

The Shapley value provides a principled framework for fairly distributing rewards among participants according to their individual contributions. While prior work has applied this concept to data valuation in machine learning, existing…

Computer Science and Game Theory · Computer Science 2026-01-22 Zhuofan Jia , Jian Pei

Variance based global sensitivity analysis measures the relevance of inputs to a single output using Sobol' indices. This paper extends the definition in a natural way to multiple outputs, directly measuring the relevance of inputs to the…

Statistics Theory · Mathematics 2025-03-25 Robert A. Milton , Solomon F. Brown

Estimating feature importance is a significant aspect of explaining data-based models. Besides explaining the model itself, an equally relevant question is which features are important in the underlying data generating process. We present a…

Machine Learning · Computer Science 2021-09-21 Pål Vegard Johnsen , Inga Strümke , Signe Riemer-Sørensen , Andrew Thomas DeWan , Mette Langaas

Interpretability of learning algorithms is crucial for applications involving critical decisions, and variable importance is one of the main interpretation tools. Shapley effects are now widely used to interpret both tree ensembles and…

Machine Learning · Statistics 2022-02-03 Clément Bénard , Gérard Biau , Sébastien da Veiga , Erwan Scornet

This study compares the performances of two sampling-based strategies for the simultaneous estimation of the first-and total-orders variance-based sensitivity indices (a.k.a Sobol' indices). The first strategy was introduced by [8] and is…

Applications · Statistics 2020-06-16 Ivano Azzini , Thierry Mara , Rossana Rosati

We introduce a variable importance measure to quantify the impact of individual input variables to a black box function. Our measure is based on the Shapley value from cooperative game theory. Many measures of variable importance operate by…

Machine Learning · Computer Science 2020-10-05 Masayoshi Mase , Art B. Owen , Benjamin Seiler

Lower-dimensional subspaces that impact estimates of uncertainty are often described by Linear combinations of input variables, leading to active variables. This paper extends the derivative-based active subspace methods and…

Numerical Analysis · Mathematics 2026-01-08 Matieyendou Lamboni , Sergei Kucherenko

Global sensitivity analysis (GSA) quantifies the influence of uncertain variables in a mathematical model. The Sobol' indices, a commonly used tool in GSA, seek to do this by attributing to each variable its relative contribution to the…

Computation · Statistics 2018-12-19 Joseph Hart , Pierre Gremaud

Researchers in explainable artificial intelligence have developed numerous methods for helping users understand the predictions of complex supervised learning models. By contrast, explaining the $\textit{uncertainty}$ of model outputs has…

Machine Learning · Statistics 2023-11-01 David S. Watson , Joshua O'Hara , Niek Tax , Richard Mudd , Ido Guy