Learning Scoring Functions with Order-Preserving Losses and Standardized Supervision

Abstract

We address the problem of designing surrogate losses for learning scoring functions in the context of label ranking. We extend to ranking problems a notion of order preserving losses previously introduced for multiclass classi?cation, and show that these losses lead to consistent formulations with respect to a family of ranking evaluation metrics. An order-preserving loss can be tailored for a given evaluation metric by appropriately setting some weights depending on this metric and the observed supervision. These weights, called the standard form of the supervision, do not always exist, but we show that previous consistency results for ranking were proved in special cases where they do. We then evaluate a new pairwise loss consistent with the (Normalized) Discounted Cumulative Gain on benchmark datasets.