Research Publications

It has been previously noted that optimization of the ncall@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 that the trade-off is a simple and intuitive function of n, k, and m (the total number of documents in a collection relevant to a query), where the diversification level decreases linearly as n approaches 1.