Related papers: Kernel-based measures of association between input…
We provide a theoretical foundation for non-parametric estimation of functions of random variables using kernel mean embeddings. We show that for any continuous function $f$, consistent estimators of the mean embedding of a random variable…
Reliability sensitivity analysis is concerned with measuring the influence of a system's uncertain input parameters on its probability of failure. Statistically dependent inputs present a challenge in both computing and interpreting these…
Generative models, like large language models, are becoming increasingly relevant in our daily lives, yet a theoretical framework to assess their generalization behavior and uncertainty does not exist. Particularly, the problem of…
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…
The global sensitivity analysis of a complex numerical model often calls for the estimation of variance-based importance measures, named Sobol' indices. Metamodel-based techniques have been developed in order to replace the cpu…
We propose two algorithms for boosting random Fourier feature models for approximating high-dimensional functions. These methods utilize the classical and generalized analysis of variance (ANOVA) decomposition to learn low-order functions,…
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…
Sensitivity analysis is an important concept to analyze the influences of parameters in a system, an equation or a collection of data. The methods used for sensitivity analysis are divided into deterministic and statistical techniques.…
Comparing multivariate yield quality distributions across spatially referenced agricultural fields is complicated by two pervasive features: non-normality and spatial autocorrelation. Classical procedures such as ANOVA, MANOVA, and standard…
Global sensitivity analysis (GSA) of numerical simulators aims at studying the global impact of the input uncertainties on the output. To perform the GSA, statistical tools based on inputs/output dependence measures are commonly used. We…
Global sensitivity analysis is a powerful set of ideas and heuristics for understanding the importance and interplay between uncertain parameters in a computational model. Such a model is characterized by a set of input parameters and an…
The estimation of variance-based importance measures (called Sobol' indices) of the input variables of a numerical model can require a large number of model evaluations. It turns to be unacceptable for high-dimensional model involving a…
Many experimental paradigms in neuroscience involve driving the nervous system with periodic sensory stimuli. Neural signals recorded using a variety of techniques will then include phase-locked oscillations at the stimulation frequency.…
Analysis of variance (ANOVA) is an extremely important method in exploratory and confirmatory data analysis. Unfortunately, in complex problems (e.g., split-plot designs), it is not always easy to set up an appropriate ANOVA. We propose a…
Regression tasks, notably in safety-critical domains, require proper uncertainty quantification, yet the literature remains largely classification-focused. In this light, we introduce a family of measures for total, aleatoric, and epistemic…
Support Vector Machines (SVMs) are an important tool for performing classification on scattered data, where one usually has to deal with many data points in high-dimensional spaces. We propose solving SVMs in primal form using feature maps…
In global sensitivity analysis, the well known Sobol' sensitivity indices aim to quantify how the variance in the output of a mathematical model can be apportioned to the different variances of its input random variables. These indices are…
Spherical and hyperspherical data are commonly encountered in diverse applied research domains, underscoring the vital task of assessing independence within such data structures. In this context, we investigate the properties of test…
We propose a framework for analyzing and comparing distributions, allowing us to design statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over…
The development of data acquisition systems is facilitating the collection of data that are apt to be modelled as functional data. In some applications, the interest lies in the identification of significant differences in group functional…