Given a set of search queries q ∈ IR Q and docu-ments d ∈ IR D , where the j th dimension of a vector indicates the occurrence of the j th word for dictionaries of size Q and D, we want to learn a score f (q, d) between a query and a given document using the model 1 We take a pairwise ranking approach to optimization.
given labeled data in the form of a set R of tuples (q, d + , d − ), where d + is a relevant (or higher ranked) document and d − an irrelevant (or lower ranked) document for query q, the goal is to find a weight matrix W ∈ IR Q×D such that f (q, d + ) > f (q, d − ) for all data tuples from R. The scoring model learns weights for all possible correspondences of query terms and document terms by directly optimizing the ranking objective at hand.