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Machine learning (ML) can be used to construct surrogate models for the fast prediction of a property of interest. ML can thus be applied to chemical projects, where the usual experimentation or calculation techniques can take hours or days…

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,…

Statistics Theory · Mathematics 2026-03-03 Troy Larsen , Alen Alexanderian

Image classification is often prone to labelling uncertainty. To generate suitable training data, images are labelled according to evaluations of human experts. This can result in ambiguities, which will affect subsequent models. In this…

Applications · Statistics 2024-07-24 Katharina Hechinger , Xiao Xiang Zhu , Göran Kauermann

In this paper we propose an extension of the classical Sobol' estimator for the estimation of variance based sensitivity indices. The approach assumes a linear correlation model between the input variables which is used to decompose the…

Methodology · Statistics 2024-08-12 Thomas Most

The deployment of Machine Learning models intraoperatively for tissue characterisation can assist decision making and guide safe tumour resections. For image classification models, pixel attribution methods are popular to infer…

Computer Vision and Pattern Recognition · Computer Science 2025-08-01 Alfie Roddan , Chi Xu , Serine Ajlouni , Irini Kakaletri , Patra Charalampaki , Stamatia Giannarou

This paper deals with neural networks modelling of HVAC systems. In order to increase the neural networks performances, a method based on sensitivity analysis is applied. The same technique is also used to compute the relevance of each…

Neural and Evolutionary Computing · Computer Science 2012-12-27 Eric Fock , Thierry Alex Mara , Alfred Jean Philippe Lauret , Harry Boyer

We define and study a generalization of Sobol sensitivity indices for the case of a vector output.

Applications · Statistics 2013-04-18 Fabrice Gamboa , Alexandre Janon , Thierry Klein , Agnès Lagnoux

In uncertainty quantification, a stochastic modelling is often applied, where parameters are substituted by random variables. We investigate linear dynamical systems of ordinary differential equations with a quantity of interest as output.…

Numerical Analysis · Mathematics 2019-09-23 Roland Pulch , Akil Narayan

Though remarkable progress has been achieved in various vision tasks, deep neural networks still suffer obvious performance degradation when tested in out-of-distribution scenarios. We argue that the feature statistics (mean and standard…

Computer Vision and Pattern Recognition · Computer Science 2022-04-25 Xiaotong Li , Yongxing Dai , Yixiao Ge , Jun Liu , Ying Shan , Ling-Yu Duan

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 $Y:=Y = f(X_1, \ldots, X_p)$…

Applications · Statistics 2013-11-15 Fabrice Gamboa , Alexandre Janon , Thierry Klein , Agnès Lagnoux

Reliable generalization metrics are fundamental to the evaluation of machine learning models. Especially in high-stakes applications where labeled target data are scarce, evaluation of models' generalization performance under distribution…

Machine Learning · Computer Science 2026-04-10 Yunxiang Peng , Mengmeng Ma , Ziyu Yao , Xi Peng

In modern engineering, physical processes are modelled and analysed using advanced computer simulations, such as finite element models. Furthermore, concepts of reliability analysis and robust design are becoming popular, hence, making…

Methodology · Statistics 2017-03-20 Roland Schöbi , Bruno Sudret

While recent computer vision algorithms achieve impressive performance on many benchmarks, they lack robustness - presented with an image from a different distribution, (e.g. weather or lighting conditions not considered during training),…

Computer Vision and Pattern Recognition · Computer Science 2021-09-28 Sebastian Cygert , Bartłomiej Wróblewski , Karol Woźniak , Radosław Słowiński , Andrzej Czyżewski

There has long been debates on how we could interpret neural networks and understand the decisions our models make. Specifically, why deep neural networks tend to be error-prone when dealing with samples that output low softmax scores. We…

Computer Vision and Pattern Recognition · Computer Science 2018-12-04 Simiao Zuo , Jialin Wu

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…

Statistics Theory · Mathematics 2025-11-10 Sébastien Da Veiga , Fabrice Gamboa , Thierry Klein , Agnès Lagnoux , Clémentine Prieur

Although recent works have brought some insights into the performance improvement of techniques used in state-of-the-art deep-learning models, more work is needed to understand their generalization properties. We shed light on this matter…

Machine Learning · Computer Science 2020-07-31 Mahsa Forouzesh , Farnood Salehi , Patrick Thiran

Predictive models that generalize well under distributional shift are often desirable and sometimes crucial to building robust and reliable machine learning applications. We focus on distributional shift that arises in causal inference from…

Machine Learning · Statistics 2018-02-27 Fredrik D. Johansson , Nathan Kallus , Uri Shalit , David Sontag

This paper presents an approach for estimating Shapley effects for use as global sensitivity metrics to quantify the relative importance of uncertain model parameters. Polynomial Chaos expansion, a well established approach for developing…

Applications · Statistics 2023-01-12 Adrian Stein , Tarunraj Singh

We present a regression technique for data-driven problems based on polynomial chaos expansion (PCE). PCE is a popular technique in the field of uncertainty quantification (UQ), where it is typically used to replace a runnable but expensive…

Machine Learning · Statistics 2019-04-02 E. Torre , S. Marelli , P. Embrechts , B. Sudret

Domain generalization (DG) aims to improve the generalizability of computer vision models toward distribution shifts. The mainstream DG methods focus on learning domain invariance, however, such methods overlook the potential inherent in…

Computer Vision and Pattern Recognition · Computer Science 2025-04-04 Shaocong Long , Qianyu Zhou , Xiangtai Li , Chenhao Ying , Yunhai Tong , Lizhuang Ma , Yuan Luo , Dacheng Tao
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