Strong and weak stability of bipartite ranking algorithms

Abstract

Ranking is an important problem in information retrieval and other applications, a good ranking algorithm should have good stability, which means for a wild change of samples, the ranking function doesn’t change too much. Among the existent ranking algorithms, the bipartite ranking is a special kind of ranking method, the goal of bipartite ranking is to learn a score function from positive and negative training samples that induces a ranking for an instance space. In this paper, the ‘almost everywhere’ stability of bipartite ranking algorithms is investigated, notions of strong stability and weak stability for bipartite ranking algorithms are defined, and the generalization bounds of stable bipartite ranking algorithms are obtained. In particular, the relationship between strong (weak) loss stability and strong (weak) score stability is also discussed.