recall at k

**Recall@K** measures **fraction of relevant items found in top-K** — evaluating what percentage of all relevant items appear in the first K results, complementing precision by measuring coverage. **What Is Recall@K?** - **Definition**: Percentage of all relevant items that appear in top-K. - **Formula**: R@K = (# relevant in top-K) / (total # relevant items). - **Range**: 0 (no relevant items found) to 1 (all relevant items in top-K). **Example** Total relevant items: 20. Top 10 results contain: 8 relevant items. - Recall@10 = 8/20 = 0.4 (40% recall). **Why Recall@K?** - **Coverage**: Measures how many relevant items are found. - **Completeness**: Important when users want comprehensive results. - **Complement to Precision**: Precision = quality, Recall = coverage. **Precision vs. Recall Trade-off** - **High Precision, Low Recall**: Few results, mostly relevant (conservative). - **Low Precision, High Recall**: Many results, some irrelevant (liberal). - **Balance**: Need both for good ranking. **When Recall@K Matters** **High Recall Important**: Research, legal discovery, medical diagnosis (can't miss relevant items). **Low Recall OK**: Quick search, single answer needed (precision more important). **Limitations** - **Requires Knowing Total Relevant**: Need to know how many relevant items exist. - **K-Dependent**: Different K values give different scores. - **Ignores Position**: Treats all top-K positions equally. **Applications**: Search evaluation, recommendation evaluation, information retrieval, document retrieval. **Tools**: scikit-learn, IR evaluation libraries. Recall@K is **essential for comprehensive retrieval** — while precision measures quality, recall measures coverage, and both are needed to fully evaluate ranking systems.