Related papers: Kernel-based ANOVA decomposition and Shapley effec…
One-dimensional Poincare inequalities are used in Global Sensitivity Analysis (GSA) to provide derivative-based upper bounds and approximations of Sobol indices. We add new perspectives by investigating weighted Poincare inequalities. Our…
Any applied mathematical model contains parameters. The paper proposes to use kernel learning for the parametric analysis of the model. The approach consists in setting a distribution on the parameter space, obtaining a finite training…
Global variance-based reliability sensitivity indices arise from a variance decomposition of the indicator function describing the failure event. The first-order indices reflect the main effect of each variable on the variance of the…
We propose a new method for input variable selection in nonlinear regression. The method is embedded into a kernel regression machine that can model general nonlinear functions, not being a priori limited to additive models. This is the…
We introduce a variable importance measure to quantify the impact of individual input variables to a black box function. Our measure is based on the Shapley value from cooperative game theory. Many measures of variable importance operate by…
Sensitivity indices are commonly used to quantity the relative inuence of any specic group of input variables on the output of a computer code. In this paper, we focus both on computer codes the output of which is a cumulative distribution…
Weighting methods are popular tools for estimating causal effects; assessing their robustness under unobserved confounding is important in practice. In the following paper, we introduce a new set of sensitivity models called "variance-based…
We consider $L^2$-approximation on weighted reproducing kernel Hilbert spaces of functions depending on infinitely many variables. We focus on unrestricted linear information, admitting evaluations of arbitrary continuous linear…
Global sensitivity analysis (GSA) is frequently used to analyze the influence of uncertain parameters in mathematical models and simulations. In principle, tools from GSA may be extended to analyze the influence of parameters in statistical…
In this article, we study nonparametric inference problems in the context of multivariate or functional time series, including testing for goodness-of-fit, the presence of a change point in the marginal distribution, and the independence of…
We present a physics-informed framework for system identification based on randomized stable atomic features. Impulse responses are represented as random superpositions of stable atoms, namely damped complex exponentials associated with…
The Shapley value concept from cooperative game theory has become a popular technique for interpreting ML models, but efficiently estimating these values remains challenging, particularly in the model-agnostic setting. Here, we revisit the…
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…
We define and study a generalization of Sobol sensitivity indices for the case of a vector output.
We consider the prediction problem of a continuous-time stochastic process on an entire time-interval in terms of its recent past. The approach we adopt is based on functional kernel nonparametric regression estimation techniques where…
Research in modern data-driven dynamical systems is typically focused on the three key challenges of high dimensionality, unknown dynamics, and nonlinearity. The dynamic mode decomposition (DMD) has emerged as a cornerstone for modeling…
This article gives a new insight of kernel-based (approximation) methods to solve the high-dimensional stochastic partial differential equations. We will combine the techniques of meshfree approximation and kriging interpolation to extend…
This study compares the performances of two sampling-based strategies for the simultaneous estimation of the first-and total-orders variance-based sensitivity indices (a.k.a Sobol' indices). The first strategy was introduced by [8] and is…
Variable importance in regression analyses is of considerable interest in a variety of fields. There is no unique method for assessing variable importance. However, a substantial share of the available literature employs Shapley values,…
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…