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Computational examples indicate that all regularization terms produce similarly good registration quality, but the cost associated with affine invariant MCM approach is, on average, less than that for others.
We compute the objective function setting all regularization parameters to zero.
In our simulations we find that, of the four structures in the ensemble, only one structure (red) is dominant for all regularization penalties.
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In this paper, all these regularization methods, as well as two combinations of them, namely, the elastic net and sparse group lasso, are presented in a unified framework.
Computational results indicate that all these regularization terms produce similarly good registration quality but that the cost associated with the AIMCM approach is, on average, less than that for the others.
All the regularization parameters were optimally tuned using a grid search from 10 − 2 to 10 through nested 5-fold cross-validation, as mentioned before.
Significance tests show that with λ1=10 and λ3=30, the sparse group lasso is significantly better than all other regularization methods under all testing conditions.
One may find out that each β k j appears in all three regularization terms.
The classifier was a set of linear one-vs-all SVMs with regularization constant C = 0.01.
In all the experiments, the regularization parameter and the other parameters in the process are heuristically adjusted until the best result is obtained.
The BL assigns the same double exponential distribution to all marker effects (conditionally on a regularization parameter), that is, where λ⩾0 is a regularization parameter.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com