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The global sensitivity analysis of a numerical model aims to quantify, by means of sensitivity indices estimate, the contributions of each uncertain input variable to the model output uncertainty. The so-called Sobol' indices, which are…

统计理论 · 数学 2019-11-26 Bertrand Iooss , Clémentine Prieur

Sensitivity indices are commonly used to quantify the relative influence of any specific group of input variables on the output of a computer code. One crucial question is then to decide whether a given set of variables has a significant…

统计理论 · 数学 2022-04-05 Thierry Klein , Nicolas Peteilh , Paul Rochet

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…

统计理论 · 数学 2025-03-25 Robert A. Milton , Solomon F. Brown

Interpreting the decisions of complex computer vision models is crucial to establish trust and accountability, especially in safety-critical domains. An established approach to interpretability is generating visual attribution maps that…

计算机视觉与模式识别 · 计算机科学 2026-04-08 David Schinagl , Christian Fruhwirth-Reisinger , Alexander Prutsch , Samuel Schulter , Horst Possegger

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…

统计理论 · 数学 2013-03-26 Alexandre Janon

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…

统计计算 · 统计学 2018-12-19 Joseph Hart , Pierre Gremaud

It is well-known that Sobol indices, which count among the most popular sensitivity indices, are based on the Sobol decomposition. Here we challenge this construction by redefining Sobol indices without the Sobol decomposition. In fact, we…

机器学习 · 统计学 2026-03-23 Gildas Mazo

As machine learning algorithms are increasingly applied to high impact yet high risk tasks, such as medical diagnosis or autonomous driving, it is critical that researchers can explain how such algorithms arrived at their predictions. In…

计算机视觉与模式识别 · 计算机科学 2021-12-06 Ruth Fong , Andrea Vedaldi

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…

This thesis explores advanced approaches to improve explainability in computer vision by analyzing and modeling the features exploited by deep neural networks. Initially, it evaluates attribution methods, notably saliency maps, by…

计算机视觉与模式识别 · 计算机科学 2025-02-04 Thomas Fel

Although neural networks can achieve very high predictive performance on various different tasks such as image recognition or natural language processing, they are often considered as opaque "black boxes". The difficulty of interpreting the…

机器学习 · 统计学 2020-01-22 Enguerrand Horel , Virgile Mison , Tao Xiong , Kay Giesecke , Lidia Mangu

Drawing parallels with the way biological networks are studied, we adapt the treatment--control paradigm to explainable artificial intelligence research and enrich it through multi-parametric input alterations. In this study, we propose a…

机器学习 · 统计学 2026-01-16 Pavel Kharyuk , Sergey Matveev , Ivan Oseledets

Semantic Segmentation is a significant research field in Computer Vision. Despite being a widely studied subject area, many visualization tools do not exist that capture segmentation quality and dataset statistics such as a class imbalance…

计算机视觉与模式识别 · 计算机科学 2023-12-19 Sourajit Saha , Shubhashis Roy Dipta

In the past decade, Sobol's variance decomposition have been used as a tool - among others - in risk management. We show some links between global sensitivity analysis and stochastic ordering theories. This gives an argument in favor of…

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…

统计计算 · 统计学 2018-04-04 Pavel Prikhodko , Nikita Kotlyarov

This paper explores the application of active learning strategies to adaptively learn Sobol indices for global sensitivity analysis. We demonstrate that active learning for Sobol indices poses unique challenges due to the definition of the…

Sensitivity analysis is an important concept to analyze the influences of parameters in a system, an equation or a collection of data. The methods used for sensitivity analysis are divided into deterministic and statistical techniques.…

其他统计学 · 统计学 2019-12-25 Eduardo Vasconcelos , Adriano Souza , Kelvin Dias

Global sensitivity analysis of a numerical code, more specifically estimation of Sobol indices associated with input variables, generally requires a large number of model runs. When those demand too much computation time, it is necessary to…

偏微分方程分析 · 数学 2012-01-16 Alexandre Janon , Maëlle Nodet , Clémentine Prieur

We propose a new importance sampling framework for the estimation and analysis of Sobol' indices. We focus on the estimation of the conditional second-moment quantity underlying these indices, which is the most challenging term to estimate.…

统计理论 · 数学 2026-03-03 Haythem Boucharif , Jérôme Morio , Paul Rochet

Global sensitivity analysis is a powerful set of ideas and heuristics for understanding the importance and interplay between uncertain parameters in a computational model. Such a model is characterized by a set of input parameters and an…

数值分析 · 数学 2020-12-23 Chun Yui Wong , Pranay Seshadri , Geoffrey T. Parks