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The selection of a range of regularization parameter values for solving a specific inverse problem is specific to that inverse problem.
In order to answer these questions, here we present a critical comparison of a wide range of regularization methods applicable to nonlinear kinetic models.
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A range of the regularization parameter, rather than one single value, can be determined.
Figure 6 c shows the prediction bias-variance trade-off for a range of the regularization parameter (see computational details in Additional file 1).
Third-order differential equations arise in a variety of problems ranging from the study of regularization of the Cauchy problem for one-dimensional hyperbolic conservation laws [1] to nano boundary layer fluid flows [2] or to describe the evolution of physical phenomena in fluctuating environments [3].
In order to demonstrate the effectiveness of our regularization method, we evaluate a tomographic reconstruction over a range of values for the regularization parameter α.
In the analysis, these hyperparameter values were set to α 1 = 1.5 and α 2 = 1 e − 4 ; this gives a relatively flat prior over a wide range of values of the regularization parameter (see Pérez et al. 2010 for further details), as S and d f were 0.19 and 5, respectively.
For the choice rule of regularization parameter, we have a range estimate for (xi_{max}) given by the following lemma.
At the same time, multi-regularization constraint reduces the sensitivity of regularization parameter in a certain range, which is beneficial to the maintenance of the complex edge penalty terms, and preserves the image edges and details.
The terms and represent two parameters that range from 0 to 1. RDA provides a fairly rich class of regularization alternatives.
To tune parameters, we perform a grid search over a range of possible parameter values and combinations of learning algorithms (SVM or LR) and type of regularization (ℓ1 or ℓ2).
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