Estimating average precision when judgments are incomplete

We consider the problem of evaluating retrieval systems with incomplete relevance judgments. Recently, Buckley and Voorhees showed that standard measures of retrieval performance are not robust to incomplete judgments, and they proposed a new measure, bpref, that is much more robust to incomplete judgments. Although bpref is highly correlated with average precision when the judgments are effectively complete, the value of bpref deviates from average precision and from its own value as the judgment set degrades, especially at very low levels of assessment. In this work, we propose three new evaluation measures induced AP, subcollection AP, and inferred AP that are equivalent to average precision when the relevance judgments are complete and that are statistical estimates of average precision when relevance judgments are a random subset of complete judgments. We consider natural …