Related papers: A new kernel-based index for the global sensitivit…
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…
We propose a novel kernel based post selection inference (PSI) algorithm, which can not only handle non-linearity in data but also structured output such as multi-dimensional and multi-label outputs. Specifically, we develop a PSI algorithm…
The Hilbert Schmidt Independence Criterion (HSIC) is a kernel dependence measure that has applications in various aspects of machine learning. Conveniently, the objectives of different dimensionality reduction applications using HSIC often…
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.…
Tabular foundation models like TabPFN and TabICL achieve state-of-the-art performance through in-context learning, yet their architectures remain fundamentally opaque. We introduce KernelICL, a framework to enhance tabular foundation models…
Sensitivity indices are commonly used to quantify the relative influence of any specific group of input variables on the output of a computer code. One crucial question is then to decide whether a given set of variables has a significant…
This paper introduces Kernel-based Information Criterion (KIC) for model selection in regression analysis. The novel kernel-based complexity measure in KIC efficiently computes the interdependency between parameters of the model using a…
In this paper, we present the general theory of embedding independence tests on Hilbert spaces that generalizes the concepts of distance covariance, distance multivariance and HSIC. This is done by defining new types of kernel on an $n$…
Recent works investigated the generalization properties in deep neural networks (DNNs) by studying the Information Bottleneck in DNNs. However, the mea- surement of the mutual information (MI) is often inaccurate due to the density…
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…
A statistical test of independence may be constructed using the Hilbert-Schmidt Independence Criterion (HSIC) as a test statistic. The HSIC is defined as the distance between the embedding of the joint distribution, and the embedding of the…
Quantifying the causal influence of input features within neural networks has become a topic of increasing interest. Existing approaches typically assess direct, indirect, and total causal effects. This work treats NNs as structural causal…
In the context of sensitivity analysis of complex phenomena in presence of uncertainty, we motivate and precise the idea of orienting the analysis towards a critical domain of the studied phenomenon. We make a brief history of related…
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…
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…
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…
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…
This work investigates the problem of testing whether $d$ functional random variables are jointly independent using a modified estimator of the $d$-variable Hilbert Schmidt Indepedence Criterion ($d$HSIC) which generalizes HSIC for the case…
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. One of the…
This article presents a general multivariate $f$-sensitivity index, rooted in the $f$-divergence between the unconditional and conditional probability measures of a stochastic response, for global sensitivity analysis. Unlike the…