Learning Preference Relations for Information Retrieval

In this paper we investigate the problem of learning a preference relation from a given set of ranked documents. We show that the Bayes's optimal decision function, when applied to learning a preference relation, may violate transitivity. This is undesirable for information retrieval, because it is in conflict with a document ranking based on the user's preferences. To overcome this problem we present a vector space based method that performs a linear mapping from documents to scalar utility values and thus guarantees transitivity. The learning of the relation between documents is formulated as a classification problem on pairs of documents and is solved using the principle of structural risk minimization for good generalization. The approach is extended to polynomial utility functions by using the potential function method (the so called "kernel trick"), which allows to incorporate higher order correlations of features into the utility function at minimal computational costs. The resu..