  Recommender systems can be formulated as a matrix completion problem,
predicting ratings from user and item parameter vectors. Optimizing these
parameters by subsampling data becomes difficult as the number of users and
items grows. We develop a novel approach to generate all latent variables on
demand from the ratings matrix itself and a fixed pool of parameters. We
estimate missing ratings using chains of evidence that link them to a small set
of prototypical users and items. Our model automatically addresses the
cold-start and online learning problems by combining information across both
users and items. We investigate the scaling behavior of this model, and
demonstrate competitive results with respect to current matrix factorization
techniques in terms of accuracy and convergence speed.
