7 Generalization Bounds for Ranking Algorithms
W. Rejchel
7.1 Introduction
We consider the ranking problem, which is popular in the machine learning community. The goal is to predict or guess the ordering between objects on the basis of their observed features. This problem has numerous applications in practice, for instance in information retrieval, banking, quality control, and survival analysis. Recently many authors have focused their attention on this subject (Freund et al., 2003; Agarwal et al., 2005; Cossock and Zhang, 2006; Rudin, 2006; Clémençon et al., 2005, 2008; Rejchel, 2012). We start this chapter with a description of the statistical framework of the ranking problem.
Let us consider two objects that are randomly selected from a population. We assume that they are described by a pair of independent and identically distributed (with respect to the measure 
) random vectors 
and 
, taking values in 
where 
is a Borel subset of
Random vectors
and
are regarded ...
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