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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

An analytic formula is proposed to characterize the variance propagation from correlated input variables to the model response, by using multi-variate Taylor series. With the formula, partial variance contributions to the model response are…

Physics and Society · Physics 2017-08-23 Yueying Zhu , Qiuping A Wang , Wei Li , Xu Cai

We establish sensitivity analysis on the sphere. We present formulas that allow us to decompose a function $f\colon \mathbb S^d\rightarrow \mathbb R$ into a sum of terms $f_{\boldsymbol u,\boldsymbol \xi}$. The index $\boldsymbol u$ is a…

Numerical Analysis · Mathematics 2026-05-15 Laura Weidensager

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

Following up on the success of the analysis of variance (ANOVA) decomposition and the Sobol indices (SI) for global sensitivity analysis, various related quantities of interest have been defined in the literature including the effective and…

Numerical Analysis · Computer Science 2017-12-06 Rafael Ballester-Ripoll , Enrique G. Paredes , Renato Pajarola

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

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

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

Although recent works have brought some insights into the performance improvement of techniques used in state-of-the-art deep-learning models, more work is needed to understand their generalization properties. We shed light on this matter…

Machine Learning · Computer Science 2020-07-31 Mahsa Forouzesh , Farnood Salehi , Patrick Thiran

The standard linear and logistic regression models assume that the response variables are independent, but share the same linear relationship to their corresponding vectors of covariates. The assumption that the response variables are…

Machine Learning · Computer Science 2019-10-09 Constantinos Daskalakis , Nishanth Dikkala , Ioannis Panageas

This article considers a novel and widely applicable approach to modeling high-dimensional dependent data when a large number of explanatory variables are available and the signal-to-noise ratio is low. We postulate that a $p$-dimensional…

Methodology · Statistics 2024-12-09 Zhaoxing Gao , Ruey S. Tsay

The R package "sensobol" provides several functions to conduct variance-based uncertainty and sensitivity analysis, from the estimation of sensitivity indices to the visual representation of the results. It implements several…

Computation · Statistics 2021-12-06 Arnald Puy , Samuele Lo Piano , Andrea Saltelli , Simon A. Levin

In this paper, we study sensitivity indices for independent groups of variables and we look at the particular case of block-additive models. We show in this case that most of the Sobol indices are equal to zero and that Shapley effects can…

Statistics Theory · Mathematics 2018-12-12 Baptiste Broto , François Bachoc , Marine Depecker , Jean-Marc Martinez

Instrumental variables regression is a tool that is commonly used in the analysis of observational data. The instrumental variables are used to make causal inference about the effect of a certain exposure in the presence of unmeasured…

Methodology · Statistics 2023-09-07 Valentin Vancak , Arvid Sjölander

In this paper, we introduce new indices adapted to outputs valued in general metric spaces. This new class of indices encompasses the classical ones; in particular, the so-called Sobol indices and the Cram{\'e}r-von-Mises indices.…

Statistics Theory · Mathematics 2021-01-21 Fabrice Gamboa , Thierry Klein , Agnès Lagnoux , Leonardo Moreno

A classical problem of statistical inference is the valid specification of a model that can account for the statistical dependencies between observations when the true structure is dense, intractable, or unknown. To address this problem, a…

Statistics Theory · Mathematics 2023-10-19 Shane Sparkes , Lu Zhang

Results from global sensitivity analysis (GSA) often guide the understanding of complicated input-output systems. Kernel-based GSA methods have recently been proposed for their capability of treating a broad scope of complex systems. In…

Methodology · Statistics 2022-08-09 John Barr , Herschel Rabitz

The use of a hypothetical generative model was been suggested for causal analysis of observational data. The very assumption of a particular model is a commitment to a certain set of variables and therefore to a certain set of possible…

Artificial Intelligence · Computer Science 2023-06-09 Nimrod Megiddo

Symbolic Data Analysis works with variables for which each unit or class of units takes a finite set of values/categories, an interval or a distribution (an histogram, for instance). When to each observation corresponds an empirical…

Methodology · Statistics 2013-05-01 Sónia Dias , Paula Brito

Recognizing, quantifying and visualizing associations between two variables is increasingly important. This paper investigates how a new function-valued measure of dependence, the quantile dependence function, can be used to construct tests…

Methodology · Statistics 2019-04-16 Ćmiel Bogdan , Ledwina Teresa