In many applications, some explanatory variables are much more expensive to collect or process than others. Preference may be given to choosing less expensive explanatory variables in the splitting process by assigning costs or scalings to be applied when considering splits. This way, the improvement made by splitting on a particular variable is downweighted by its cost in determining the final split.
Other times in practice, the consequences are greater for misclassifying one class over another. Therefore, it is possible to give preference for correctly classifying certain classes, or even assigning specific costs to how an observation is misclassified, that is, which wrong class it falls in.
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