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Adaptive hyperparameter selection in kernel-based partition of unity methods by global optimization techniques.

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Title: Adaptive hyperparameter selection in kernel-based partition of unity methods by global optimization techniques.
Authors: Cavoretto, Roberto1,2 (AUTHOR) roberto.cavoretto@unito.it, De Rossi, Alessandra1,2 (AUTHOR) alessandra.derossi@unito.it, Haider, Adeeba1,2 (AUTHOR) adeeba.haider@unito.it, Sergeyev, Yaroslav D.2,3,4 (AUTHOR) yaro@dimes.unical.it
Source: Soft Computing - A Fusion of Foundations, Methodologies & Applications. Apr2025, Vol. 29 Issue 7, p3733-3748. 16p.
Subjects: Partition of unity method, Computational mathematics, Global optimization, Radial basis functions, Mathematical optimization
Abstract: In this article, we present a new numerical algorithm to detect the kernel shape parameter and the subdomain radius size within a partition of unity method for scattered data interpolation. Since an adaptive search of such hyperparameters is quite expensive from the computational point of view, we propose the use of a leave-one-out cross-validation (LOOCV) technique combined with univariate global optimization tools from the class of Lipschitz derivative-free methods. Conventional LOOCV methods often suffer from ill-conditioning, particularly in high-dimensional settings, leading to computational inefficiencies. To address these issues, we consider efficient global optimization strategies characterized by optimistic and pessimistic improvements. The resulting algorithm allows us to improve the performance of the standard approach in terms of both accuracy and efficiency. Numerical results deriving from the study of some test cases and an application to real-world data support our analysis. [ABSTRACT FROM AUTHOR]
Copyright of Soft Computing - A Fusion of Foundations, Methodologies & Applications is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: In this article, we present a new numerical algorithm to detect the kernel shape parameter and the subdomain radius size within a partition of unity method for scattered data interpolation. Since an adaptive search of such hyperparameters is quite expensive from the computational point of view, we propose the use of a leave-one-out cross-validation (LOOCV) technique combined with univariate global optimization tools from the class of Lipschitz derivative-free methods. Conventional LOOCV methods often suffer from ill-conditioning, particularly in high-dimensional settings, leading to computational inefficiencies. To address these issues, we consider efficient global optimization strategies characterized by optimistic and pessimistic improvements. The resulting algorithm allows us to improve the performance of the standard approach in terms of both accuracy and efficiency. Numerical results deriving from the study of some test cases and an application to real-world data support our analysis. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Soft Computing - A Fusion of Foundations, Methodologies & Applications is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s00500-025-10624-w
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        Text: English
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      – SubjectFull: Partition of unity method
        Type: general
      – SubjectFull: Computational mathematics
        Type: general
      – SubjectFull: Global optimization
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      – SubjectFull: Radial basis functions
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      – SubjectFull: Mathematical optimization
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              M: 04
              Text: Apr2025
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              Y: 2025
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