From Ranking to Classification: A Statistical View
In applications related to information retrieval, the goal is not only to build a classifier for deciding whether a document x among a list χ is relevant or not, but to learn a scoring function s : χ → ℝ for ranking all possible documents with respect to their relevancy. Here we show how the bipartite ranking problem boils down to binary classification with dependent data when accuracy is measured by the A U C criterion. The natural estimate of the risk being of the form of a U-statistic, consistency of methods based on empirical risk minimization is studied using the theory of U-processes. Taking advantage of this specific form, we prove that fast rates of convergence may be achieved under general noise assumptions.