An adaptive residual sub-sampling algorithm for kernel interpolation based on maximum likelihood estimations

Cavoretto, Roberto; Rossi, Alessandra De

doi:10.1016/j.cam.2022.114658

Cited by 15 publications

(2 citation statements)

References 18 publications

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“…However, there exist also some approaches that can give us a prediction of ε via an error estimate. The most commonly used techniques oriented to address this issue are based on power function, cross validation and maximum likelihood estimation criteria (see [1,39,40]).…”

Section: Choosing Shape Parameters Via Loocvmentioning

confidence: 99%

Adaptive Hyperparameter Selection in Kernel-based Partition of Unity Methods by Global Optimization Techniques

Cavoretto,

De Rossi,

Haider

et al. 2024

Preprint

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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 technique combined with univariate global optimization tools from the class of Lipschitz derivative-free method. Particularly, 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. MSC Classification: 65D05 , 65D15 , 90C26 , 65K05

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Section: Choosing Shape Parameters Via Loocvmentioning

confidence: 99%

Adaptive Hyperparameter Selection in Kernel-based Partition of Unity Methods by Global Optimization Techniques

Cavoretto,

De Rossi,

Haider

et al. 2024

Preprint

View full text Add to dashboard Cite

show abstract

“…Furthermore, RBFs can model non-linear relationships between input and output variables, making them appropriate for applications where linear models are not sufficient. This flexibility arises from the choice of non-linear basis functions used in RBFs [8,9]. This paper investigates how to improve the computational efficiency and, especially, the convergence order of approximations without increasing the stencil size.…”

Section: Introduction 1goalsmentioning

confidence: 99%

Efficient Fourth-Order Weights in Kernel-Type Methods without Increasing the Stencil Size with an Application in a Time-Dependent Fractional PDE Problem

Liu,

Shateyi

2024

Mathematics

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An effective strategy to enhance the convergence order of nodal approximations in interpolation or PDE problems is to increase the size of the stencil, albeit at the cost of increased computational burden. In this study, our goal is to improve the convergence orders for approximating the first and second derivatives of sufficiently differentiable functions using the radial basis function-generated Hermite finite-difference (RBF-HFD) scheme. By utilizing only three equally spaced points in 1D, we are able to boost the convergence rate to four. Extensive tests have been conducted to demonstrate the effectiveness of the proposed theoretical weighting coefficients in solving interpolation and PDE problems.

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An Improved Adaptive Meshless Refinement for the RBF-FD Method for 2D Elliptic Equations

Dang

2024

Vietnam J. Math.

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An adaptive residual sub-sampling algorithm for kernel interpolation based on maximum likelihood estimations

Cited by 15 publications

References 18 publications

Adaptive Hyperparameter Selection in Kernel-based Partition of Unity Methods by Global Optimization Techniques

Adaptive Hyperparameter Selection in Kernel-based Partition of Unity Methods by Global Optimization Techniques

Efficient Fourth-Order Weights in Kernel-Type Methods without Increasing the Stencil Size with an Application in a Time-Dependent Fractional PDE Problem

An Improved Adaptive Meshless Refinement for the RBF-FD Method for 2D Elliptic Equations

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