Generalization Bounds of Ranking via Query-Level Stability I

The quality of ranking determines the success or failure of information retrieval and the goal of ranking is to learn a real-valued ranking function that induces a ranking or ordering over an instance space. We focus on generalization ability of learning to rank algorithms for information retrieval (IR). The contribution of this paper is to give generalization bounds for such ranking algorithm via uniform (strong and weak) query-level stability by deleting one element from sample set or change one element in sample set. Only we define the corresponding definitions and list all the lemmas we need. All results will show in "Generalization Bounds of Ranking via Query-Level Stability II".