On the Mathematical Relationship between Expected n-call@k and the Relevance vs. Diversity Trade-off
This provides a theoretical foundation for understanding diversification in information retrieval, though it is incremental as it builds on prior observations.
The paper formally quantifies the relationship between expected n-call@k and the relevance-diversity trade-off, showing that diversification increases as n approaches 1, with the trade-off being a simple function independent of k.
It has been previously noted that optimization of the n-call@k relevance objective (i.e., a set-based objective that is 1 if at least n documents in a set of k are relevant, otherwise 0) encourages more result set diversification for smaller n, but this statement has never been formally quantified. In this work, we explicitly derive the mathematical relationship between expected n-call@k and the relevance vs. diversity trade-off --- through fortuitous cancellations in the resulting combinatorial optimization, we show the trade-off is a simple and intuitive function of n (notably independent of the result set size k e n), where diversification increases as n approaches 1.