相关论文: Higher order Sobol' indices
In this paper we propose an extension of the classical Sobol' estimator for the estimation of variance based sensitivity indices. The approach assumes a linear correlation model between the input variables which is used to decompose the…
This article explores the generalized analysis-of-variance or ANOVA dimensional decomposition (ADD) for multivariate functions of dependent random variables. Two notable properties, stemming from weakened annihilating conditions, reveal…
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…
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…
In this paper, we first study a new sensitivity index that is based on higher moments and generalizes the so-called Sobol one. Further, following an idea of Borgonovo ([3]), we define and study a new sensitivity index based on the…
Global sensitivity analysis is used to quantify the influence of uncertain input parameters on the response variability of a numerical model. The common quantitative methods are applicable to computer codes with scalar input variables. This…
The FANOVA (or "Sobol'-Hoeffding") decomposition of multivariate functions has been used for high-dimensional model representation and global sensitivity analysis. When the objective function f has no simple analytic form and is costly to…
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…
Consider a subset $A$ of $\mathbb{F}_p^n$ and a decomposition of its indicator function as the sum of two bounded functions $1_A=f_1+f_2$. For every family of linear forms, we find the smallest degree of uniformity $k$ such that assuming…
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…
Global sensitivity analysis is a set of methods aiming at quantifying the contribution of an uncertain input parameter of the model (or combination of parameters) on the variability of the response. We consider here the estimation of the…
This paper makes the case for using Shapley value to quantify the importance of random input variables to a function. Alternatives based on the ANOVA decomposition can run into conceptual and computational problems when the input variables…
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…
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.…
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…
A new method for estimating Sobol' indices is proposed. The new method makes use of 3 independent input vectors rather than the usual 2. It attains much greater accuracy on problems where the target Sobol' index is small, even outperforming…
New global sensitivity measures based on quantiles of the output are introduced. Such measures can be used for global sensitivity analysis of problems in which quantiles are explicitly the functions of interest and for identification of…
We extend recent higher order concentration results in the discrete setting to include functions of possibly dependent variables whose distribution (on the product space) satisfies a logarithmic Sobolev inequality with respect to a…
We study the higher Frobenius-Schur indicators of modules over semisimple Hopf algebras, and relate them to other invariants as the exponent, the order, and the index. We prove various divisibility and integrality results for these…
In this paper we propose a method for the approximation of high-dimensional functions over finite intervals with respect to complete orthonormal systems of polynomials. An important tool for this is the multivariate classical analysis of…