Ralf Herbirch, Thore Graepel, Peter Bollmann-Sdorra, and Klaus Obermayer
In this paper we investigate the problem of learning a preference relation i~om 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 documeats to scalar utility values and thus guarantees transitivity. The learning of the relation between documeats 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 resulting algorithm is tested on aa example with artificial data. The algorithm successfully learns the utility function underlying the training examples and shows good classification performance.