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We describe a novel attribution method which is grounded in Sensitivity Analysis and uses Sobol indices. Beyond modeling the individual contributions of image regions, Sobol indices provide an efficient way to capture higher-order…

Computer Vision and Pattern Recognition · Computer Science 2022-02-17 Thomas Fel , Remi Cadene , Mathieu Chalvidal , Matthieu Cord , David Vigouroux , Thomas Serre

This paper presents a simple noise correction method for Sobol' indices estimation. Sobol' indices, especially total Sobol' indices are quite sensitive to the noise in the output and tend to be severly biased (overestimated) if no noise…

Computation · Statistics 2018-04-04 Pavel Prikhodko , Nikita Kotlyarov

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

A novel theoretical and numerical framework for the estimation of Sobol sensitivity indices for models in which inputs are confined to a non-rectangular domain (e.g., in presence of inequality constraints) is developed. Two numerical…

Statistics Theory · Mathematics 2016-05-18 S. Kucherenko , O. V. Klymenko , N. Shah

Biomechanical models often need to describe very complex systems, organs or diseases, and hence also include a large number of parameters. One of the attractive features of physics-based models is that in those models (most) parameters have…

Computational Engineering, Finance, and Science · Computer Science 2023-01-10 Barbara Wirthl , Sebastian Brandstaeter , Jonas Nitzler , Bernhard A. Schrefler , Wolfgang A. Wall

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

Predictions from science and engineering models depend on several input parameters. Global sensitivity analysis quantifies the importance of each input parameter, which can lead to insight into the model and reduced computational cost;…

Numerical Analysis · Mathematics 2016-07-28 Paul G. Constantine , Paul Diaz

Complex computer codes are widely used in science and engineering to model physical phenomena. Furthermore, it is common that they have a large number of input parameters. Global sensitivity analysis aims to identify those which have the…

Statistics Theory · Mathematics 2013-07-09 Loic Le Gratiet , Claire Cannamela , Bertrand Iooss

Sobol' sensitivity index estimators for stochastic models are functions of nested Monte Carlo estimators, which are estimators built from two nested Monte Carlo loops. The outer loop explores the input space and, for each of the…

Statistics Theory · Mathematics 2024-03-20 Henri Mermoz Kouye , Gildas Mazo

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

This paper addresses sensitivity analysis for dynamic models, linking dependent inputs to observed outputs. The usual method to estimate Sobol indices are based on the independence of input variables. We present a method to overpass this…

Applications · Statistics 2015-09-15 Mathilde Grandjacques , Alexandre Janon , Benoit Delinchant , Olivier Adrot

The presence of uncertainties are inevitable in engineering design and analysis, where failure in understanding their effects might lead to the structural or functional failure of the systems. The role of global sensitivity analysis in this…

Computation · Statistics 2017-10-24 Pramudita Satria Palar , Lavi Rizki Zuhal , Koji Shimoyama , Takeshi Tsuchiya

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

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 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

Global sensitivity analysis is now established as a powerful approach for determining the key random input parameters that drive the uncertainty of model output predictions. Yet the classical computation of the so-called Sobol' indices is…

Computation · Statistics 2016-06-16 L. Le Gratiet , S. Marelli , B. Sudret

In the context of computer code experiments, sensitivity analysis of a complicated input-output system is often performed by ranking the so-called Sobol indices. One reason of the popularity of Sobol's approach relies on the simplicity of…

Statistics Theory · Mathematics 2018-10-30 R. Fraiman , F. Gamboa , L. Moreno

Computational models of the cardiovascular system are increasingly used for the diagnosis, treatment, and prevention of cardiovascular disease. Before being used for translational applications, the predictive abilities of these models need…

Applications · Statistics 2024-01-11 Friederike Schäfer , Daniele E. Schiavazzi , Leif Rune Hellevik , Jacob Sturdy

The variance-based method of Sobol sensitivity indices is very popular among practitioners due to its efficiency and easiness of interpretation. However, for high-dimensional models the direct application of this method can be very time…

Statistics Theory · Mathematics 2016-05-26 S. Kucherenko , S. Song

There exist many methods for sensitivity analysis readily available to the practitioner. While each seeks to help the modeler answer the same general question -- How do sources of uncertainty or changes in the model inputs relate to…

Methodology · Statistics 2025-06-16 Devin Francom , Abigael Nachtsheim