Learning Bregman Distance Functions for Structural Learning to Rank

We study content-based learning to rank from the perspective of learning distance functions. Standardly, the two key issues of learning to rank, feature mappings and score functions, are usually modeled separately, and the learning is usually restricted to modeling a linear distance function such as the Mahalanobis distance. However, the modeling of feature mappings and score functions are mutually interacted, and the patterns underlying the data are probably complicated and nonlinear. Thus, as a general nonlinear distance family, the Bregman distance is a suitable distance function for learning to rank, due to its strong generalization ability for distance functions, and its nonlinearity for exploring the general patterns of data distributions. In this paper, we study learning to rank as a structural learning problem, and devise a Bregman distance function to build the ranking model based on structural SVM. To improve the model robustness to outliers, we develop a robust structural learning framework for the ranking model. The proposed model Robust Structural Bregman distance functions Learning to Rank (RSBLR) is a general and unified framework for learning distance functions to rank. The experiments of data ranking on real-world datasets show the superiority of this method to the state-of-the-art literature, as well as its robustness to the noisily labeled outliers.