Catalog Coverage

Definition

Catalog Coverage

Catalog coverage is a beyond-accuracy metric that assesses the percentage of unique items in the entire catalog that are actually recommended to users across all recommendation lists. It indicates the breadth of exposure a system provides: how much of the item inventory ever reaches a user. A system that always recommends a small set of popular items has low coverage, leaving a large portion of the catalog completely unexposed.

Intuition

How much of the shelf do users ever see?

Accuracy metrics (Recall, Precision, NDCG) only ask whether the items shown were correct. They are blind to the items that were never shown at all. A recommender can score perfectly on accuracy while recommending the same handful of blockbuster items to every user.

Coverage takes the provider / catalog side view: pool together every item that appears in any user’s top-K list, and ask what fraction of the whole catalog that represents. High coverage means the system distributes exposure broadly; low coverage means most of the Long Tail stays invisible. This directly connects to Popularity Bias and Item Fairness — a popularity-skewed model amplifies the long-tail distribution and exposes only the popular head.

Mathematical Formulation

The simplest (and lecture-presented) form is item-space coverage: the size of the union of all recommended items relative to the catalog size.

$\text{Catalog Coverage}=\frac{|{\bigcup }_{u\in U}{\text{TopK}}_u|}{|I|}=\frac{\text{Number of unique recommended items}}{\text{Total number of items in the catalog}}$

where:

• $U$ — the set of all users
• ${\text{TopK}}_u$ — the top-$K$ recommendation list produced for user $u$
• ${\bigcup }_{u\in U}{\text{TopK}}_u$ — the set of distinct items recommended to at least one user (a union, so an item recommended to many users is counted once)
• $I$ — the full item catalog; $|I|$ is its cardinality
• range: $[0,1]$ — higher ($\uparrow$) is better; $1.0$ means every catalog item was recommended to someone

Key Properties / Variants

• Direction: higher is better ($\uparrow$). It is a beyond-accuracy objective, often in tension with accuracy (see Diversity vs accuracy trade-off below).
• Union, not sum: because of the union over users, an item recommended to 1 user and an item recommended to 1,000,000 users contribute identically. Plain catalog coverage therefore measures whether an item is exposed, not how often — it can hide severe exposure inequality among the items that are covered.
• Distinguish from Diversity: diversity (e.g. Intra-List Distance, category Entropy, Gini) is measured within a single list — variety for one user. Coverage is a system-level / aggregate property across all lists. A system can give each user a diverse list yet still cover only a small slice of the catalog (every user gets the same diverse set).
• Sensitivity to $K$ and to $|U|$: larger top-$K$ lists or more users mechanically increase the union and inflate coverage; comparisons must fix $K$ and the user set.
• Common related variants (beyond the strict item-space form above):
  • Prediction coverage — fraction of items for which the model can produce a score/prediction at all (relevant to Cold Start items that have no interactions).
  • Gini / entropy of the recommendation-frequency distribution — captures how evenly exposure is spread across the covered items (the “how often” that plain coverage ignores), linking coverage to exposure-inequality measures.

Algorithm: Catalog Coverage (item-space)
─────────────────────────────────────────
Input: catalog I, users U, model, list size K
recommended_set ← ∅            # union accumulator
for each user u in U:
    TopK_u ← recommend(model, u, K)   # top-K items for u
    recommended_set ← recommended_set ∪ TopK_u
coverage ← |recommended_set| / |I|
return coverage

Coverage ≠ fair exposure

A high coverage number does not guarantee fair exposure. Because coverage uses a set union, it only checks that each item was shown at least once; it says nothing about the distribution of attention. Two systems with identical 100% coverage can differ enormously: one may show every item roughly equally, another may show one item to almost everyone and the rest to a single user each. To capture how much exposure each item receives — accounting for the decreasing attention users pay at deeper rank positions (a browsing model) — use exposure-based Item Fairness metrics (MinMaxRatio, Max-Min Fairness) rather than coverage alone.

Connections

• Beyond-accuracy sibling of: Diversity, Novelty, Serendipity
• Contrasts with: Recall, Precision, NDCG (accuracy-only metrics ignore unexposed items)
• Caused/worsened by: Popularity Bias, the Long Tail distribution, Cold Start items
• Provider-side concern within: Fairness in Recommendation, specifically Item Fairness / Exposure Fairness
• Within-list counterpart: Intra-List Distance, Entropy (per-list variety vs system-wide breadth)
• Trade-off context: Filter Bubble / Echo Chamber formation when coverage collapses

Appears In

• RS-L02 - Evaluation Beyond Accuracy