Collaborative Kalman Filtering for Dynamic Matrix Factorization

We propose a new algorithm for estimation, prediction, and recommendation named the collaborative Kalman filter. Suited for use in collaborative filtering settings encountered in recommendation systems with significant temporal dynamics in user preferences, the approach extends probabilistic matrix factorization in time through a state-space model. This leads to an estimation procedure with parallel Kalman filters and smoothers coupled through item factors. Learning of global parameters uses the expectation-maximization algorithm. The method is compared to existing techniques and performs favorably on both generated data and real-world movie recommendation data.