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The more/less concentrated designation is based on the ranking of the 1997 concentration ratio and choosing a break point that maximizes the marginal size of decreases in the concentration numbers in moving from more- to less-concentrated industries.
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Since W it is missing, maximizing the marginal likelihood appears to be the most natural estimation approach.
In step 4 of MAMK CP (Algorithm 3), in order to maximize the marginal gain, we have to compute σ(C i ∪C j ) for all the communities C j ∈ P, thus, MAMK CP requires O ( n 2 τ ) time to obtain a K-VDP when n is large and K is small.
As estimates of α, β, we use the values maximizing the marginal likelihood given the estimates, and.
To learn this model, we also need to maximize the marginal likelihood of the labels C n.
Here, we use L-BFGS to maximize the marginal likelihood due to its fast convergence and low-memory consumption.
The hyperparameters, i.e. the variances, are estimated through maximizing the marginal likelihood, and the variables with zero variance estimates are pruned from the model.
Therefore, we instead estimate the parameters by maximizing the marginal probability of the labels as below: (3) The results produced by HLR are still region-level classification.
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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