Related papers: Randomized pick-freeze for sparse Sobol indices es…
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…
Let $X:=(X_1, \ldots, X_p)$ be random objects (the inputs), defined on some probability space $(\Omega,{\mathcal{F}}, \mathbb P)$ and valued in some measurable space $E=E_1\times\ldots \times E_p$. Further, let $Y:=Y = f(X_1, \ldots, X_p)$…
Sobol' indices measure the dependence of a high dimensional function on groups of variables defined on the unit cube $[0,1]^d$. They are based on the ANOVA decomposition of functions, which is an $L^2$ decomposition. In this paper we…
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…
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…
Stochastic models are necessary for the realistic description of an increasing number of applications. The ability to identify influential parameters and variables is critical to a thorough analysis and understanding of the underlying…
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…
The Sobol' indices are a recognized tool in global sensitivity analysis. When the uncertain variables in a model are statistically independent, the Sobol' indices may be easily interpreted and utilized. However, their interpretation and…
Sobol' sensitivity indices allow to quantify the respective effects of random input variables and their combinations on the variance of mathematical model output. We focus on the problem of Sobol' indices estimation via a metamodeling…
In the context of global sensitivity analysis, the Sobol' indices constitute a powerful tool for assessing the relative significance of the uncertain input parameters of a model. We herein introduce a novel approach for evaluating these…
The hierarchically orthogonal functional decomposition of any measurable function f of a random vector X=(X_1,...,X_p) consists in decomposing f(X) into a sum of increasing dimension functions depending only on a subvector of X. Even when…
In this work we are interested in the problems of supervised learning and variable selection when the input-output dependence is described by a nonlinear function depending on a few variables. Our goal is to consider a sparse nonparametric…
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…
Penalized regression models such as the Lasso have proved useful for variable selection in many fields - especially for situations with high-dimensional data where the numbers of predictors far exceeds the number of observations. These…
Factor importance measures the impact of each feature on output prediction accuracy. Many existing works focus on the model-based importance, but an important feature in one learning algorithm may hold little significance in another model.…
A parameter estimation method is devised for a slow-fast stochastic dynamical system, where often only the slow component is observable. By using the observations only on the slow component, the system parameters are estimated by working on…
In this paper we develop a novel approach for estimating large and sparse dynamic factor models using variational inference, also allowing for missing data. Inspired by Bayesian variable selection, we apply slab-and-spike priors onto the…
Global sensitivity analysis (GSA) aims at quantifying the contribution of input variables over the variability of model outputs. In the frame of functional outputs, a common goal is to compute sensitivity maps (SM), i.e sensitivity indices…
Insightful visualization of multidimensional scalar fields, in particular parameter spaces, is key to many fields in computational science and engineering. We propose a principal component-based approach to visualize such fields that…
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…