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(a) Irregular scenario and (b) regularized scenario.
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To deal with network irregularities, the parameter tuning problem is solved on a cell-by-cell basis by aggregating the results from multiple regularized scenarios built on a per-adjacency basis.
However, in two cases we observe that the worst case regularization scenario performed worse than the non-regularized case.
In each case, the medium and the best case regularization scenarios clearly outperformed the non-regularized estimation, leading to better generalizable calibrated models.
The regularized optimization is solved for a set of regularization parameters in each scenario and depending on the amount of data at hand the generalized cross validation method (GCV) – for larger dataset– or the robust generalized cross-validation method (RGCV) – for smaller dataset– is recommended to choose the optimal candidate.
In such distributed scenario, the training problem can be formulated as the (regularized) optimization of a non-convex social cost function, given by the sum of local (non-convex) costs, where each agent contributes with a single error term defined with respect to its local dataset.
However, we also observe larger bias from the nominal trajectory for the regularized models, since no prior knowledge was used in this case (worst case scenario).
For instance, at P T = 30 dBW the regularized channel inversion in the feed space generates a 111% relative throughput increase with respect to the reference scenario, and 17% with respect to the same processing in the beam space.
The next summer, the dance became more regularized.
The Bank Holiday Act of 1871 further regularized leisure time.
The phone companies would no longer coöperate with the F.B.I. unless there was some regularized scheme.
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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