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Integrating advanced communication protocols in production has accelerated the adoption of data-driven predictive quality methods, notably machine learning (ML) models. However, ML models in image classification often face significant…

Machine Learning · Computer Science 2026-02-04 Lukas Bahr , Lucas Poßner , Konstantin Weise , Sophie Gröger , Rüdiger Daub

In global sensitivity analysis, the well known Sobol' sensitivity indices aim to quantify how the variance in the output of a mathematical model can be apportioned to the different variances of its input random variables. These indices are…

Statistics Theory · Mathematics 2018-01-11 Nazih Benoumechiara , Kevin Elie-Dit-Cosaque

Growing model complexities in load modeling have created high dimensionality in parameter estimations, and thereby substantially increasing associated computational costs. In this paper, a tensor-based method is proposed for identifying…

Optimization and Control · Mathematics 2020-03-10 You Lin , Yishen Wang , Jianhui Wang , Siqi Wang , Di Shi

The main objective of this paper is to estimate optimally Sobol' indices at any order when a unique input/output i.i.d.\ sample is available. Our approach stands on three main ingredients: semi-parametric estimation theory, high-order…

Statistics Theory · Mathematics 2025-11-10 Sébastien Da Veiga , Fabrice Gamboa , Thierry Klein , Agnès Lagnoux , Clémentine Prieur

In the context of air quality control, our objective is to quantify the impact of uncertain inputs such as meteorological conditions and traffic parameters on pollutant dispersion maps. It is worth noting that the majority of sensitivity…

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

Variance-based global sensitivity analysis (GSA) can provide a wealth of information when applied to complex models. A well-known Achilles' heel of this approach is its computational cost which often renders it unfeasible in practice. An…

Numerical Analysis · Mathematics 2026-01-08 John Darges , Alen Alexanderian , Pierre Gremaud

Uncertainties exist in both physics-based and data-driven models. Variance-based sensitivity analysis characterizes how the variance of a model output is propagated from the model inputs. The Sobol index is one of the most widely used…

Methodology · Statistics 2020-06-09 Zhanlin Liu , Youngjun Choe

We propose to estimate a metamodel and the sensitivity indices of a complex model m in the Gaussian regression framework. Our approach combines methods for sensitivity analysis of complex models and statistical tools for sparse…

Statistics Theory · Mathematics 2019-11-19 Sylvie Huet , Marie-Luce Taupin

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. One of the…

Probability · Mathematics 2018-11-21 Pierre Etoré , Clémentine Prieur , Dang Khoi Pham , Long Li

Parameter-dependent models arise in many contexts such as uncertainty quantification, sensitivity analysis, inverse problems or optimization. Parametric or uncertainty analyses usually require the evaluation of an output of a model for many…

Numerical Analysis · Mathematics 2018-10-22 Anthony Nouy

We propose and assess a new global (derivative-free) optimization algorithm, inspired by the LIPO algorithm, which uses variance-based sensitivity analysis (Sobol indices) to reduce the number of calls to the objective function. This method…

Optimization and Control · Mathematics 2019-06-13 Alexandre Janon

In the context of sensitivity analysis of complex phenomena in presence of uncertainty, we motivate and precise the idea of orienting the analysis towards a critical domain of the studied phenomenon. We make a brief history of related…

Methodology · Statistics 2018-04-02 Hugo Raguet , Amandine Marrel

The Trotter-Suzuki decomposition is one of the main approaches for realization of quantum simulations on digital quantum computers. Variance-based global sensitivity analysis (the Sobol method) is a wide used method which allows to…

Quantum Physics · Physics 2021-01-12 Alexey N. Pyrkov , Yurii Zotov , Jiangyu Cui , Manhong Yung

Let $X:=(X_1, \ldots, X_p)$ be random objects (the inputs), defined on some probability space $(\Omega,{\mathcal{F}}, \mathbb P)$ and valued in some measurable space $E=E_1\times\ldots \times E_p$. Further, let $Y:=Y = f(X_1, \ldots, X_p)$…

Applications · Statistics 2013-11-15 Fabrice Gamboa , Alexandre Janon , Thierry Klein , Agnès Lagnoux

We propose a new statistical estimation framework for a large family of global sensitivity analysis methods. Our approach is based on rank statistics and uses an empirical correlation coefficient recently introduced by Sourav Chatterjee. We…

Statistics Theory · Mathematics 2023-06-29 Fabrice Gamboa , Pierre Gremaud , Thierry Klein , Agnès Lagnoux

Tensor methods are among the most prominent tools for the numerical solution of high-dimensional problems where functions of multiple variables have to be approximated. These methods exploit the tensor structure of function spaces and apply…

Numerical Analysis · Mathematics 2021-02-01 Anthony Nouy

We present an HSIC-based approach for global sensitivity analysis of broad classes of models with correlated and possibly function-valued inputs and outputs. To this end, we define the total HSIC sensitivity index: a bounded, interpretable,…

Statistics Theory · Mathematics 2026-03-03 Troy Larsen , Alen Alexanderian

Global sensitivity analysis is the main quantitative technique for identifying the most influential input variables in a numerical simulation model. In particular when the inputs are independent, Sobol' sensitivity indices attribute a…

Statistics Theory · Mathematics 2021-01-15 Sébastien da Veiga

This study demonstrates the capabilities of several methods for analyzing the sensitivity of neural networks to perturbations of the input data and interpreting their underlying mechanisms. The investigated approaches include the Sobol…

Numerical Analysis · Mathematics 2025-04-22 Jiaxuan Miao , Sergey Matveev