Extending average precision to graded relevance judgments

Evaluation metrics play a critical role both in the context of comparative evaluation of the performance of retrieval systems and in the context of learning-to-rank (LTR) as objective functions to be optimized. Many different evaluation metrics have been proposed in the IR literature, with average precision (AP) being the dominant one due a number of desirable properties it possesses. However, most of these measures, including average precision, do not incorporate graded relevance. In this work, we propose a new measure of retrieval effectiveness, the Graded Average Precision (GAP). GAP generalizes average precision to the case of multi-graded relevance and inherits all the desirable characteristics of AP: it has a nice probabilistic interpretation, it approximates the area under a graded precision-recall curve and it can be justified in terms of a simple but moderately plausible user model. We then evaluate GAP in …