Error bound of magnitude-preserving ranking with Fredholm kernel

Data-dependent Fredholm kernel has attracted much attention in machine learning literatures for its flexibility to utilize the empirical information. However, the previous theoretical results are limited to the classification or density ratio estimation problems. In this paper, we extend the framework of learning with Fredholm kernel to the ranking setting. A new magnitude-preserving ranking with Fredholm kernel is proposed, and its generalization error analysis is established by using the concentrate estimate techniques. The derived result implies that the proposed method can achieve the satisfactory learning rate with polynomial decay.