Precision@k and Recall@k

The problem, from first principles

Search and recommendation systems return a ranked list, and only the top few results are ever seen. Precision@k asks how much of the top k is relevant; Recall@k asks how much of everything relevant made it into the top k.

From theory to code

Implement precision_at_k(ranked, relevant, k) and recall_at_k(ranked, relevant, k).

Constraints

• ranked is a list of item ids, best first; relevant is a collection of the truly relevant ids.
• precision_at_k divides by k even if ranked is shorter than k; return 0.0 when k <= 0.
• recall_at_k divides by the number of relevant items; return 0.0 when there are none, or when k <= 0.
• Both return Python floats.

Hints

Open one at a time. Each gives away a little more than the last.