  Advanced and effective collaborative filtering methods based on explicit
feedback assume that unknown ratings do not follow the same model as the
observed ones (\emph{not missing at random}). In this work, we build on this
assumption, and introduce a novel dynamic matrix factorization framework that
allows to set an explicit prior on unknown values. When new ratings, users, or
items enter the system, we can update the factorization in time independent of
the size of data (number of users, items and ratings). Hence, we can quickly
recommend items even to very recent users. We test our methods on three large
datasets, including two very sparse ones, in static and dynamic conditions. In
each case, we outrank state-of-the-art matrix factorization methods that do not
use a prior on unknown ratings.
