Ranking with ordered weighted pairwise classification

In ranking with the pairwise classification approach, the loss associated to a predicted ranked list is the mean of the pairwise classification losses. This loss is inadequate for tasks like information retrieval where we prefer ranked lists with high precision on the top of the list. We propose to optimize a larger class of loss functions for ranking, based on an ordered weighted average (OWA) (Yager, 1988) of the classification losses. Convex OWA aggregation operators range from the max to the mean depending on their weights, and can be used to focus on the top ranked elements as they give more weight to the largest losses. When aggregating hinge losses, the optimization problem is similar to the SVM for interdependent output spaces. Moreover, we show that OWA aggregates of margin-based classification losses have good generalization properties. Experiments on the Letor 3.0 benchmark dataset for information retrieval validate our approach.