Related papers: Sensitivity analysis for multidimensional and func…
Uncertainties exist in both physics-based and data-driven models. Variance-based sensitivity analysis characterizes how the variance of a model output is propagated from the model inputs. The Sobol index is one of the most widely used…
Sobolev quantities (norms, inner products, and distances) of probability density functions are important in the theory of nonparametric statistics, but have rarely been used in practice, partly due to a lack of practical estimators. They…
The coefficients of elastic and dissipative operators in a linear hyperbolic SPDE are jointly estimated using multiple spatially localised measurements. As the resolution level of the observations tends to zero, we establish the asymptotic…
Physical phenomena are commonly modeled by numerical simulators. Such codes can take as input a high number of uncertain parameters and it is important to identify their influences via a global sensitivity analysis (GSA). However, these…
Complex computer codes are widely used in science and engineering to model physical phenomena. Furthermore, it is common that they have a large number of input parameters. Global sensitivity analysis aims to identify those which have the…
In this article, we construct semiparametrically efficient estimators of linear functionals of a probability measure in the presence of side information using an easy empirical likelihood approach. We use estimated constraint functions and…
Given-data methods for variance-based sensitivity analysis have significantly advanced the feasibility of Sobol' index computation for computationally expensive models and models with many inputs. However, the limitations of existing…
We present an approach to defining Hilbert spaces of functions depending on infinitely many variables or parameters, with emphasis on a weighted tensor product construction based on stable space splittings, The construction has been used in…
High-dimensional functional data have become increasingly prevalent in modern applications such as high-frequency financial data and neuroimaging data analysis. We investigate a class of high-dimensional linear regression models, where each…
We prove weak convergence in a separable Hilbert space for estimators of high-dimensional regression coefficients, which yields asymptotic normality and enables direct use of standard asymptotic tools such as the continuous mapping theorem.…
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…
Sensitivity analysis is an important part of a mathematical modeller's toolbox for model analysis. In this review paper, we describe the most frequently used sensitivity techniques, discussing their advantages and limitations, before…
Global sensitivity analysis aims at quantifying the impact of input variability onto the variation of the response of a computational model. It has been widely applied to deterministic simulators, for which a set of input parameters has a…
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…
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…
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.…
In this paper, we consider the problem of parameter sensitivity in models of complex dynamical systems through the lens of information geometry. We calculate the sensitivity of model behavior to variations in parameters. In most cases,…
We present an HSIC-based approach for global sensitivity analysis of broad classes of models with correlated and possibly function-valued inputs and outputs. To this end, we define the total HSIC sensitivity index: a bounded, interpretable,…
Variance-based Sobol' sensitivity is one of the most well-known measures in global sensitivity analysis (GSA). However, uncertainties with certain distributions, such as highly skewed distributions or those with a heavy tail, cannot be…
Using tools from the theory of operator ideals and s-numbers, we develop a general approach to transfer estimates for $L_2$ -approximation of Sobolev functions into estimates for $L_\infty$-approximation, with precise control of all…