Combining Ordinal Preferences by Boosting

We analyze the relationship between ordinal ranking and binary classification with a new technique called reverse reduction. In particular, we prove that the regret can be transformed between ordinal ranking and binary classification. The proof allows us to establish a general equivalence between the two in terms of hardness. Furthermore, we use the technique to design a novel boosting approach that improves any cost-sensitive base ordinal ranking algorithm. The approach extends the well-known AdaBoost to the area of ordinal ranking, and inherits many of its good properties. Experimental results demonstrate that our proposed approach can achieve decent training and test performance even when the base algorithm produces only simple decision stumps.