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I would like to create a rank predictor (e.g. 1-20).

I'm wondering whether I should use classification or regression algorithm for that?

As there is ordering between classes then it kind of makes sense to use some kind of regression, but on the other hand the output should be limited to [1-20]. Is there some third option for that? One limitation is that I would need to use something already implemented (like scikit-learn) because of time constraint.

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In principle this can be done with ordinal regression, which comes in several different forms depending on the assumptions you make about the relative distances between the categories and how those distances are related to the values of the predictors. A quick search found this implementation of some approaches following the scikit-learn API.

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