Defazio, AaronCaetano, Tiberio2015-12-10June 26-Ju9781450312851http://hdl.handle.net/1885/68699Item neighbourhood methods for collaborative filtering learn a weighted graph over the set of items, where each item is connected to those it is most similar to. The prediction of a user's rating on an item is then given by that rating of neighbouring items, weighted by their similarity. This paper presents a new neighbourhood approach which we call item fields, whereby an undirected graphical model is formed over the item graph. The resulting prediction rule is a simple generalization of the classical approaches, which takes into account non-local information in the graph, allowing its best results to be obtained when using drastically fewer edges than other neighbourhood approaches. A fast approximate maximum entropy training method based on the Bethe approximation is presented, which uses a simple gradient ascent procedure. When using precomputed sufficient statistics on the Movielens datasets, our method is faster than maximum likelihood approaches by two orders of magnitude.Keywords: Bethe approximation; Classical approach; Collaborative filtering; Data sets; Gradient ascent; GraphicaL model; Maximum entropy; Maximum likelihood approaches; Neighbourhood; Nonlocal; Orders of magnitude; Prediction rules; Sufficient statistics; TrainingA graphical model formulation of collaborative filtering neighbourhood methods with fast maximum entropy training20122016-02-24