pub fn combmin<I: Clone + Eq + Hash>(
results_a: &[(I, f32)],
results_b: &[(I, f32)],
) -> Vec<(I, f32)>Expand description
CombMIN: minimum score across all lists.
Formula: score(d) = min(s_r(d)) for all retrievers r containing d.
§Historical Context
CombMIN emerged from the information retrieval meta-search literature of the late 1990s alongside CombSUM, CombMAX, and CombMNZ. The “Comb” family was systematically studied by Fox & Shaw (1994) and later by Lee (1997).
| Method | Formula | Intuition |
|---|---|---|
| CombSUM | Σ s_r(d) | Agreement across all retrievers |
| CombMAX | max s_r(d) | At least one retriever likes it |
| CombMIN | min s_r(d) | All retrievers agree (conservative) |
| CombMNZ | Σ s_r(d) × count | Reward overlap explicitly |
§When to Use CombMIN
- High-precision requirements: When false positives are costly
- Consensus retrieval: Only surface documents all systems agree on
- Spam filtering: A document must pass multiple filters
CombMIN is inherently conservative: a document with scores [0.9, 0.1] gets score 0.1, while CombMAX would give 0.9.
§Caution
Documents appearing in only one list will have that single score as their CombMIN. To require presence in multiple lists, combine with a threshold on occurrence count.
§Reference
Fox & Shaw, “Combination of Multiple Searches”, NIST TREC 1994. Lee, “Analyses of Multiple Evidence Combination”, SIGIR 1997.