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2 results on '"Toulemonde, Gwladys"'

1. High-dimensional variable clustering based on sub-asymptotic maxima of a weakly dependent random process

Author

Boulin, Alexis, Di Bernardino, Elena, Laloë, Thomas, Toulemonde, Gwladys, Littoral, Environment: MOdels and Numerics (LEMON), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Montpelliérain Alexander Grothendieck (IMAG), Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Hydrosciences Montpellier (HSM), Institut de Recherche pour le Développement (IRD)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Institut de Recherche pour le Développement (IRD)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Jean Alexandre Dieudonné (LJAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA), Institut Montpelliérain Alexander Grothendieck (IMAG), Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM), Université de Montpellier (UM), Centre National de la Recherche Scientifique (CNRS), ANR-20-CE23-0011,McLaren,Apprentissage Statistique et Evaluation du Risque(2020), ANR-19-P3IA-0002,3IA@cote d'azur,3IA Côte d'Azur(2019), Université Côte d'Azur (UCA), and IMAG

Subjects
FOS: Computer and information sciences, 60G70, 62H05, 62M99, Consistent estimation, Extreme value theory, Mathematics - Statistics Theory, Machine Learning (stat.ML), Statistics Theory (math.ST), Variable clustering, Methodology (stat.ME), Statistics - Machine Learning, High dimensional models, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], FOS: Mathematics, MSC Codes: 60G70, 62H05, 62M99, Statistics - Methodology
Abstract

We propose a new class of models for variable clustering called Asymptotic Independent block (AI-block) models, which defines population-level clusters based on the independence of the maxima of a multivariate stationary mixing random process among clusters. This class of models is identifiable, meaning that there exists a maximal element with a partial order between partitions, allowing for statistical inference. We also present an algorithm for recovering the clusters of variables without specifying the number of clusters \emph{a priori}. Our work provides some theoritical insights into the consistency of our algorithm, demonstrating that under certain conditions it can effectively identify clusters in the data with a computational complexity that is polynomial in the dimension. This implies that groups can be learned nonparametrically in which block maxima of a dependent process are only sub-asymptotic., Comment: 50 pages, 6 figures

Published
2023
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2. Hierarchical space-time modeling of exceedances with an application to rainfall data

Author

Bacro, Jean-Noel, Gaetan, Carlo, OPITZ, Thomas, Toulemonde, Gwladys, Institut Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Dipartimento di Scienze Ambientali, Informatica e Statistica [Venezia] (DAIS), University of Ca’ Foscari [Venice, Italy], Biostatistique et Processus Spatiaux (BIOSP), Institut National de la Recherche Agronomique (INRA), Littoral, Environnement : Méthodes et Outils Numériques (LEMON), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Biostatistique et Processus Spatiaux (BioSP), Littoral, Environment: MOdels and Numerics (LEMON), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Montpelliérain Alexander Grothendieck (IMAG), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Hydrosciences Montpellier (HSM), and Institut de Recherche pour le Développement (IRD)-Institut national des sciences de l'Univers (INSU - CNRS)-Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS)-Institut de Recherche pour le Développement (IRD)-Institut national des sciences de l'Univers (INSU - CNRS)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Methodology (stat.ME), FOS: Computer and information sciences, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Statistics - Methodology, ComputingMilieux_MISCELLANEOUS
Abstract

The statistical modeling of space-time extremes in environmental applications is key to understanding complex dependence structures in original event data and to generating realistic scenarios for impact models. In this context of high-dimensional data, we propose a novel hierarchical model for high threshold exceedances defined over continuous space and time by embedding a space-time Gamma process convolution for the rate of an exponential variable, leading to asymptotic independence in space and time. Its physically motivated anisotropic dependence structure is based on geometric objects moving through space-time according to a velocity vector. We demonstrate that inference based on weighted pairwise likelihood is fast and accurate. The usefulness of our model is illustrated by an application to hourly precipitation data from a study region in Southern France, where it clearly improves on an alternative censored Gaussian space-time random field model. While classical limit models based on threshold-stability fail to appropriately capture relatively fast joint tail decay rates between asymptotic dependence and classical independence, strong empirical evidence from our application and other recent case studies motivates the use of more realistic asymptotic independence models such as ours.

Published
2017
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