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This reveals that (L_1) regularization results in slightly lower misfit than (L_2) regularization, although both approaches describe almost all of the variance in the measurements.
Unfortunately, similar to compressed sensing formulations for solving under-determined linear systems of equations [19], such a regularization results in a nonconvex optimization problem that is NP-hard to solve and motivates relaxing the ℓ0- norm with its closest convex approximation, namely, the ℓ1- norm.
The results are in agreement with the intuition that a lower regularization results in larger prediction variance and less bias.
The RSS grows with α since larger regularization results in a worse fit to the data (see Fig. 5 a).
Using an augmented cost function and optimizing regularization results in better performance compared to pixel based and unregularized shape based approach measured in terms of MSE and spatial localization as measured using the Dice coefficient and Symmetric difference.
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Second, the entropy term provides regularization, resulting in more consistent and robust learning when compared to deterministic methods.
In [7], an approach was proposed to treat the uncertain RS imaging problems that unifies the MR spectral estimation strategy with the worst case statistical performance (WCSP) optimization-based convex regularization resulting in the descriptive experiment design regularization (DEDR) method.
Thus, enforcing model sparsity using L1-regularization resulted in dropping the feature of presence in a cleft or pocket, but retained residue centrality and solvent accessibility which allow this defining characteristic of active site residues to be recognized.
In Section 3, we give the regularization results for the regularized model (1.3) and obtain the maximum principle.
Weakening the regularization strength results in vulnerability to the random error of measurements, but such influence can be reduced by increasing averaging or exposure time of the camera measurement.
Larger regularization parameter results in an estimated parameter vector closer to the reference parameter vector and therefore smaller penalty, but worse fit to the calibration data.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com