1. Definition
- User Coverage measures what fraction of users actually receive recommendations (or useful recommendations) from a system.
- It tells us how inclusive the recommender is: does it work for everyone, or only for a subset of “easy” users?
2. Formula
Let:
- $U$ = total set of users in the system.
- $U_{rec}$ = set of users for whom the system can produce at least one valid recommendation.
Then:
$\text{User Coverage} = \frac{|U_{rec}|}{|U|}$
- Sometimes expressed as a percentage.
3. Example
Suppose:
- Total users = 1,000.
- Recommender successfully generates lists for 950.
- The other 50 are new users (no history → cold-start problem).
$\text{User Coverage} = \frac{950}{1000} = 0.95 \; (95\%)$
4. Intuition
- High user coverage: almost everyone gets recommendations → the system is robust, even for new or sparse users.
- Low user coverage: system only works for users with rich histories or certain profiles.
5. Variants
- Top-N User Coverage: percentage of users who receive at least N items in their recommendation list.
- Quality-based User Coverage: fraction of users who receive recommendations above some quality threshold (e.g., precision ≥ 0.3).
6. Relation to Other Metrics
- Item Coverage: focuses on breadth of items recommended; User Coverage focuses on breadth of users served.
- Cold-start analysis: low user coverage often signals the recommender struggles with new users.
- Fairness: ensuring all user groups (e.g., demographics) are covered.
Summary:
User Coverage = proportion of users for whom the system can provide at least one valid recommendation. It captures how broadly the system serves its user base and highlights cold-start or sparsity issues.