Modeling Relevance as a Function of Retrieval Rank

Batched evaluations in IR experiments are commonly built using relevance judgments formed over a sampled pool of documents. However, judgment coverage tends to be incomplete relative to the metrics being used to compute effectiveness, since collection size often makes it financially impractical to judge every document. As a result, a considerable body of work has arisen exploring the question of how to fairly compare systems in the face of unjudged documents. Here we consider the same problem from another perspective, and investigate the relationship between relevance likelihood and retrieval rank, seeking to identify plausible methods for estimating document relevance and hence computing an inferred gain. A range of models are fitted against two typical TREC datasets, and evaluated both in terms of their goodness of fit relative to the full set of known relevance judgments, and also in terms of their predictive ability when shallower initial pools are presumed, and extrapolated metric scores are computed based on models developed from those shallow pools.