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We show how to apply Sobol's method of global sensitivity analysis to measure the influence exerted by a set of nodes' evidence on a quantity of interest expressed by a Bayesian network. Our method exploits the network structure so as to…

Machine Learning · Statistics 2021-10-11 Rafael Ballester-Ripoll , Manuele Leonelli

Sensitivity analysis (SA) is a procedure for studying how sensitive are the output results of large-scale mathematical models to some uncertainties of the input data. The models are described as a system of partial differential equations.…

Numerical Analysis · Mathematics 2017-01-20 Ivan Dimov , Rayna Georgieva

As deep vision models' popularity rapidly increases, there is a growing emphasis on explanations for model predictions. The inherently explainable attribution method aims to enhance the understanding of model behavior by identifying the…

Computer Vision and Pattern Recognition · Computer Science 2024-08-07 Xianren Zhang , Dongwon Lee , Suhang Wang

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

In a model of the form $Y=h(X_1,\ldots,X_d)$ where the goal is to estimate a parameter of the probability distribution of $Y$, we define new sensitivity indices which quantify the importance of each variable $X_i$ with respect to this…

Methodology · Statistics 2013-05-13 Jean-Claude Fort , Thierry Klein , Nabil Rachdi

Most of the current boundary detection systems rely exclusively on low-level features, such as color and texture. However, perception studies suggest that humans employ object-level reasoning when judging if a particular pixel is a…

Computer Vision and Pattern Recognition · Computer Science 2015-09-22 Gedas Bertasius , Jianbo Shi , Lorenzo Torresani

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 main objective of this paper is to propose a new approach for estimating the entire collection of Sobol' indices simultaneously. Our approach exploits the fact that Sobol' indices can be rewritten as solutions to an optimization problem…

Statistics Theory · Mathematics 2025-12-09 Manon Costa , Sébastien Gadat , Xavier Gendre , Thierry Klein

A variety of indices aim to quantify the impact of input variables on a response, typically the output from a complex computer code or black-box model. Most commonly used, the Sobol' index typically measures the influence of some inputs…

Statistics Theory · Mathematics 2025-07-22 Thierry Klein , Agnès Lagnoux , Paul Rochet , Thi Mong Ngoc Nguyen

Explaining recommendations enables users to understand whether recommended items are relevant to their needs and has been shown to increase their trust in the system. More generally, if designing explainable machine learning models is key…

Machine Learning · Computer Science 2020-08-27 Darius Afchar , Romain Hennequin

Sobol indices are a widespread quantitative measure for variance-based global sensitivity analysis, but computing and utilizing them remains challenging for high-dimensional systems. We propose the tensor train decomposition (TT) as a…

Numerical Analysis · Computer Science 2017-12-04 Rafael Ballester-Ripoll , Enrique G. Paredes , Renato Pajarola

Fully supervised salient object detection (SOD) methods have made considerable progress in performance, yet these models rely heavily on expensive pixel-wise labels. Recently, to achieve a trade-off between labeling burden and performance,…

Computer Vision and Pattern Recognition · Computer Science 2023-06-12 Binwei Xu , Haoran Liang , Weihua Gong , Ronghua Liang , Peng Chen

The variance-based method of global sensitivity indices based on Sobol sensitivity indices became very popular among practitioners due to its easiness of interpretation. For complex practical problems computation of Sobol indices generally…

Numerical Analysis · Mathematics 2016-06-03 Sergei Kucherenko , Shufang Song

This paper presents a new efficient black-box attribution method based on Hilbert-Schmidt Independence Criterion (HSIC), a dependence measure based on Reproducing Kernel Hilbert Spaces (RKHS). HSIC measures the dependence between regions of…

Computer Vision and Pattern Recognition · Computer Science 2022-09-28 Paul Novello , Thomas Fel , David Vigouroux

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

eXplainable Artificial Intelligence (XAI) has emerged as an essential requirement when dealing with mission-critical applications, ensuring transparency and interpretability of the employed black box AI models. The significance of XAI spans…

Computer Vision and Pattern Recognition · Computer Science 2023-11-28 Hossein Shreim , Abdul Karim Gizzini , Ali J. Ghandour

Weakly supervised object localization (WSOL) aims at predicting object locations in an image using only image-level category labels. Common challenges that image classification models encounter when localizing objects are, (a) they tend to…

Computer Vision and Pattern Recognition · Computer Science 2022-04-15 Saurav Gupta , Sourav Lakhotia , Abhay Rawat , Rahul Tallamraju

In recent years, neural networks have demonstrated their remarkable ability to discern intricate patterns and relationships from raw data. However, understanding the inner workings of these black box models remains challenging, yet crucial…

Machine Learning · Statistics 2024-04-18 Niklas Koenen , Marvin N. Wright

The Variogram Analysis of Response Surfaces (VARS) has been proposed by Razavi and Gupta as a new comprehensive framework in sensitivity analysis. According to these authors, VARS provides a more intuitive notion of sensitivity and it is…

Applications · Statistics 2020-11-24 Arnald Puy , Samuele Lo Piano , Andrea Saltelli

Neural network visualization techniques mark image locations by their relevancy to the network's classification. Existing methods are effective in highlighting the regions that affect the resulting classification the most. However, as we…

Computer Vision and Pattern Recognition · Computer Science 2020-12-04 Shir Gur , Ameen Ali , Lior Wolf