Tensor Algorithms for Advanced Sensitivity Metrics

Following up on the success of the analysis of variance (ANOVA) decomposition and the Sobol indices (SI) for global sensitivity analysis, various related quantities of interest have been defined in the literature, including the effective and mean dimensions, the dimension distribution, and the Shapl...

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Detalles Bibliográficos
Autores: Paredes, Enrique, Pajarola, Renato, Ballester Ripoll, Rafael
Tipo de recurso: artículo
Fecha de publicación:2018
País:España
Institución:IE
Repositorio:Repositorio IE
OAI Identifier:oai:repositorio.ie.edu:20.500.14417/4024
Acceso en línea:https://doi.org/10.1137/17M1160252
https://hdl.handle.net/20.500.14417/4024
https://epubs.siam.org/doi/10.1137/17M1160252
Access Level:acceso abierto
Palabra clave:variance-based sensitivity analysis
surrogate modeling
tensor train decomposition
Sobol indices
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spelling Tensor Algorithms for Advanced Sensitivity MetricsParedes, EnriquePajarola, RenatoBallester Ripoll, Rafaelvariance-based sensitivity analysissurrogate modelingtensor train decompositionSobol indicesFollowing up on the success of the analysis of variance (ANOVA) decomposition and the Sobol indices (SI) for global sensitivity analysis, various related quantities of interest have been defined in the literature, including the effective and mean dimensions, the dimension distribution, and the Shapley values. Such metrics combine up to exponential numbers of SI in different ways and can be of great aid in uncertainty quantification and model interpretation tasks, but are computationally challenging. We focus on surrogate-based sensitivity analysis for independently distributed variables, namely, via the tensor train (TT) decomposition. This format permits flexible and scalable surrogate modeling and can efficiently extract all SI at once in a compressed TT representation of their own. Based on this, we contribute a range of novel algorithms that compute more advanced sensitivity metrics by selecting and aggregating certain subsets of SI in the tensor compressed domain. Drawing on an interpretation of the TT model in terms of deterministic finite automata, we are able to construct explicit auxiliary TT tensors that encode exactly all necessary index selection masks. Having both the SI and the masks in the TT format allows efficient computation of all aforementioned metrics, as we demonstrate in a number of example models.YesPublishedSociety for Industrial and Applied Mathematicshttps://ror.org/02jjdwm7520252018info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://doi.org/10.1137/17M1160252https://hdl.handle.net/20.500.14417/4024https://epubs.siam.org/doi/10.1137/17M1160252reponame:Repositorio IEinstname:IEInglésIE School of Science & TechnologyIE UniversityApplied MathematicsAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:repositorio.ie.edu:20.500.14417/40242026-06-15T12:40:57Z
dc.title.none.fl_str_mv Tensor Algorithms for Advanced Sensitivity Metrics
title Tensor Algorithms for Advanced Sensitivity Metrics
spellingShingle Tensor Algorithms for Advanced Sensitivity Metrics
Paredes, Enrique
variance-based sensitivity analysis
surrogate modeling
tensor train decomposition
Sobol indices
title_short Tensor Algorithms for Advanced Sensitivity Metrics
title_full Tensor Algorithms for Advanced Sensitivity Metrics
title_fullStr Tensor Algorithms for Advanced Sensitivity Metrics
title_full_unstemmed Tensor Algorithms for Advanced Sensitivity Metrics
title_sort Tensor Algorithms for Advanced Sensitivity Metrics
dc.creator.none.fl_str_mv Paredes, Enrique
Pajarola, Renato
Ballester Ripoll, Rafael
author Paredes, Enrique
author_facet Paredes, Enrique
Pajarola, Renato
Ballester Ripoll, Rafael
author_role author
author2 Pajarola, Renato
Ballester Ripoll, Rafael
author2_role author
author
dc.contributor.none.fl_str_mv https://ror.org/02jjdwm75
dc.subject.none.fl_str_mv variance-based sensitivity analysis
surrogate modeling
tensor train decomposition
Sobol indices
topic variance-based sensitivity analysis
surrogate modeling
tensor train decomposition
Sobol indices
description Following up on the success of the analysis of variance (ANOVA) decomposition and the Sobol indices (SI) for global sensitivity analysis, various related quantities of interest have been defined in the literature, including the effective and mean dimensions, the dimension distribution, and the Shapley values. Such metrics combine up to exponential numbers of SI in different ways and can be of great aid in uncertainty quantification and model interpretation tasks, but are computationally challenging. We focus on surrogate-based sensitivity analysis for independently distributed variables, namely, via the tensor train (TT) decomposition. This format permits flexible and scalable surrogate modeling and can efficiently extract all SI at once in a compressed TT representation of their own. Based on this, we contribute a range of novel algorithms that compute more advanced sensitivity metrics by selecting and aggregating certain subsets of SI in the tensor compressed domain. Drawing on an interpretation of the TT model in terms of deterministic finite automata, we are able to construct explicit auxiliary TT tensors that encode exactly all necessary index selection masks. Having both the SI and the masks in the TT format allows efficient computation of all aforementioned metrics, as we demonstrate in a number of example models.
publishDate 2018
dc.date.none.fl_str_mv 2018
2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://doi.org/10.1137/17M1160252
https://hdl.handle.net/20.500.14417/4024
https://epubs.siam.org/doi/10.1137/17M1160252
url https://doi.org/10.1137/17M1160252
https://hdl.handle.net/20.500.14417/4024
https://epubs.siam.org/doi/10.1137/17M1160252
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv IE School of Science & Technology
IE University
Applied Mathematics
dc.rights.none.fl_str_mv Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
publisher.none.fl_str_mv Society for Industrial and Applied Mathematics
dc.source.none.fl_str_mv reponame:Repositorio IE
instname:IE
instname_str IE
reponame_str Repositorio IE
collection Repositorio IE
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,812429

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