On generalized cross validation for stable parameter selection in disease models

2015 ◽  
Vol 23 (5) ◽  
Author(s):  
Alexandra Smirnova ◽  
Maia Martcheva ◽  
Hui Liu
Keyword(s):  
Inverse Problem ◽  
Operator Equation ◽  
Recovery Rate ◽  
Cross Validation ◽  
Regularization Parameter ◽  
Parameter Selection ◽  
Time Dependent ◽  
Disease Models ◽  
Generalized Cross Validation ◽  
Irregular Operator

AbstractIn this paper we study advantages and limitations of the Generalized Cross Validation (GCV) approach for selecting a regularization parameter in the case of a partially stochastic linear irregular operator equation. The research has been motivated by an inverse problem in epidemiology, where the goal was to reconstruct a time dependent treatment recovery rate for

scholarly journals Inverse Problem Solution and Regularization Parameter Selection for Current Distribution Reconstruction in Switching Arcs by Inverting Magnetic Fields

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Jinlong Dong ◽  
Guogang Zhang ◽  
Zhiqiang Zhang ◽  
Yingsan Geng ◽  
Jianhua Wang
Keyword(s):  
Inverse Problem ◽  
Density Distribution ◽  
Current Density ◽  
Cross Validation ◽  
Regularization Parameter ◽  
Current Density Distribution ◽  
Optimality Criteria ◽  
Parameter Selection ◽  
Selection Strategies ◽  
Regularization Parameter Selection

Current density distribution in electric arcs inside low voltage circuit breakers is a crucial parameter for us to understand the complex physical behavior during the arcing process. In this paper, we investigate the inverse problem of reconstructing the current density distribution in arcs by inverting the magnetic fields. A simplified 2D arc chamber is considered. The aim of this paper is the computational side of the regularization method, regularization parameter selection strategies, and the estimation of systematic error. To address the ill-posedness of the inverse problem, Tikhonov regularization is analyzed, with the regularization parameter chosen by Morozov’s discrepancy principle, the L-curve, the generalized cross-validation, and the quasi-optimality criteria. The provided range of regularization parameter selection strategies is much wider than in the previous works. Effects of several features on the performance of these criteria have been investigated, including the signal-to-noise ratio, dimension of measurement space, and the measurement distance. The numerical simulations show that the generalized cross-validation and quasi-optimality criteria provide a more satisfactory performance on the robustness and accuracy. Moreover, an optimal measurement distance can be expected when using a planner sensor array to perform magnetic measurements.

scholarly journals A New Method for Optimal Regularization Parameter Determination in the Inverse Problem of Load Identification

2016 ◽  
Vol 2016 ◽  
pp. 1-16 ◽  
Author(s):  
Wei Gao ◽  
Kaiping Yu ◽  
Ying Wu
Keyword(s):  
Inverse Problem ◽  
Regularization Method ◽  
Cross Validation ◽  
Regularization Parameter ◽  
New Method ◽  
Parameter Determination ◽  
Load Identification ◽  
Noise Levels ◽  
Regularization Parameters ◽  
Curve Method

According to the regularization method in the inverse problem of load identification, a new method for determining the optimal regularization parameter is proposed. Firstly, quotient function (QF) is defined by utilizing the regularization parameter as a variable based on the least squares solution of the minimization problem. Secondly, the quotient function method (QFM) is proposed to select the optimal regularization parameter based on the quadratic programming theory. For employing the QFM, the characteristics of the values of QF with respect to the different regularization parameters are taken into consideration. Finally, numerical and experimental examples are utilized to validate the performance of the QFM. Furthermore, the Generalized Cross-Validation (GCV) method and theL-curve method are taken as the comparison methods. The results indicate that the proposed QFM is adaptive to different measuring points, noise levels, and types of dynamic load.

Sign in / Sign up

Export Citation Format

Share Document