Comments (1)
For those that came here from Google.
I think it is easier to understand if we first explain recall at k:
If the number of items is greater than k, then the recall can never reach one, not even with a recommender that knows the test set. Let's say you have only one user that has 12 interactions with items. With k=5 the maximum recall is 5/12, as you will only get 5 recommendations.
The MAP uses the precision-recall curve, and in a perfect recommender is just equivalent to the number of recovered elements, which is the recall. Therefore, the maximum MAP achievable is equivalent to the maximum recall achievable, which probably is not 1.
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