Learning Label Preferences: Ranking Error Versus Position Error

We consider the problem of learning a ranking function, that is a mapping from instances to rankings over a finite number of labels. Our learning method, referred to as ranking by pairwise comparison (RPC), first induces pairwise order relations from suitable training data, using a natural extension of so-called pairwise classification. A ranking is then derived from a set of such relations by means of a ranking procedure. This paper elaborates on a key advantage of such a decomposition, namely the fact that our learner can be adapted to different loss functions by using different ranking procedures on the same underlying order relations. In particular, the Spearman rank correlation is minimized by using a simple weighted voting procedure. Moreover, we discuss a loss function suitable for settings where candidate labels must be tested successively until a target label is found, and propose a ranking procedure for minimizing the corresponding risk.