Precision and Recall at K

Score a ranked list of recommendations with precision at k and recall at k.

A recommender shows a user only the top few items, so the metrics look only at the top k. Let hits be the number of the first k recommended items that are in the user's set of relevant items. Then

precision@k = hits / k
recall@k    = hits / len(relevant)

Precision asks how much of what you showed was useful. Recall asks how much of what was useful you showed.

Function signature

def precision_recall_at_k(recommended, relevant, k):

Example

Input

recommended = [3, 1, 7, 5, 2]
relevant    = {1, 2, 9}
precision_recall_at_k(recommended, relevant, k=3)

Output

(0.3333333333, 0.3333333333)

Reasoning

The top 3 items are 3, 1, 7. Only 1 is relevant, so hits = 1. Precision is 1 / 3 and recall is 1 / 3, since there are 3 relevant items. Item 2 is relevant but ranked fifth, so it does not count at k = 3.

Constraints and notes

• recommended is a list of item ids in rank order with no repeats.
• If recommended has fewer than k items, still divide precision by k.
• If relevant is empty, recall is 0.0.
• Return a tuple of two floats.