  Matrix factorization from a small number of observed entries has recently
garnered much attention as the key ingredient of successful recommendation
systems. One unresolved problem in this area is how to adapt current methods to
handle changing user preferences over time. Recent proposals to address this
issue are heuristic in nature and do not fully exploit the time-dependent
structure of the problem. As a principled and general temporal formulation, we
propose a dynamical state space model of matrix factorization. Our proposal
builds upon probabilistic matrix factorization, a Bayesian model with Gaussian
priors. We utilize results in state tracking, such as the Kalman filter, to
provide accurate recommendations in the presence of both process and
measurement noise. We show how system parameters can be learned via
expectation-maximization and provide comparisons to current published
techniques.
