Related papers: A new kernel-based index for the global sensitivit…
We propose the Sobolev Independence Criterion (SIC), an interpretable dependency measure between a high dimensional random variable X and a response variable Y . SIC decomposes to the sum of feature importance scores and hence can be used…
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…
Global sensitivity analysis of complex numerical models can be performed by calculating variance-based importance measures of the input variables, such as the Sobol indices. However, these techniques, requiring a large number of model…
Global sensitivity analysis with variance-based measures suffers from several theoretical and practical limitations, since they focus only on the variance of the output and handle multivariate variables in a limited way. In this paper, we…
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…
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 $Y:=Y = f(X_1, \ldots, X_p)$…
Biomechanical models often need to describe very complex systems, organs or diseases, and hence also include a large number of parameters. One of the attractive features of physics-based models is that in those models (most) parameters have…
Measuring and testing the dependency between multiple random functions is often an important task in functional data analysis. In the literature, a model-based method relies on a model which is subject to the risk of model misspecification,…
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…
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…
A new non parametric approach to the problem of testing the independence of two random process is developed. The test statistic is the Hilbert Schmidt Independence Criterion (HSIC), which was used previously in testing independence for…
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…
We propose a new statistical estimation framework for a large family of global sensitivity analysis indices. Our approach is based on rank statistics and uses an empirical correlation coefficient recently introduced by Chatterjee [9]. We…
Causal inference grows increasingly complex as the number of confounders increases. Given treatments $X$, confounders $Z$ and outcomes $Y$, we develop a non-parametric method to test the \textit{do-null} hypothesis $H_0:\; p(y|\text{\it…
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…
Global sensitivity analysis aims at determining which uncertain input parameters of a computational model primarily drives the variance of the output quantities of interest. Sobol' indices are now routinely applied in this context when the…
The problem of adaptive multivariate function estimation in the single-index regression model with random design and weak assumptions on the noise is investigated. A novel estimation procedure that adapts simultaneously to the unknown index…
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…
Traditionally, the sensitivity analysis of a Bayesian network studies the impact of individually modifying the entries of its conditional probability tables in a one-at-a-time (OAT) fashion. However, this approach fails to give a…
The deployment of deep learning models in critical domains necessitates a balance between high accuracy and interpretability. We introduce SIC, an inherently interpretable neural network that provides local and global explanations of its…