On the Mathematical Relationship between Expected ncall@k and the Relevance vs. Diversity Tradeoff
Abstract
It has been previously noted that optimization of the ncall@k relevance objective (i.e., a setbased 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 ncall@k and the relevance vs. diversity tradeoff  through fortuitous cancellations in the resulting combinatorial optimization, we show the tradeoff 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.
 Publication:

arXiv eprints
 Pub Date:
 September 2016
 DOI:
 10.48550/arXiv.1609.06568
 arXiv:
 arXiv:1609.06568
 Bibcode:
 2016arXiv160906568L
 Keywords:

 Computer Science  Information Retrieval
 EPrint:
 SIGIR short paper