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Tensor Algorithms for Advanced Sensitivity Metrics


Ballester-Ripoll, Rafael; Paredes, Enrique G; Pajarola, R (2018). Tensor Algorithms for Advanced Sensitivity Metrics. SIAM/ASA Journal on Uncertainty Quantification, 6(3):1172-1197.

Abstract

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.

Abstract

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Informatics
Dewey Decimal Classification:000 Computer science, knowledge & systems
Uncontrolled Keywords:visualization, data analytics, tensor approximation, multidimensional data, surrogate modeling, sobol indices, sensitivity analysis
Language:English
Date:2018
Deposited On:20 Feb 2019 16:43
Last Modified:25 Sep 2019 00:09
Publisher:Society for Industrial and Applied Mathematics
ISSN:2166-2525
Additional Information:The final publication is available at SIAM via https://doi.org/10.1137/17M1160252
OA Status:Green
Publisher DOI:https://doi.org/10.1137/17M1160252
Other Identification Number:merlin-id:17262

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