  Matrix completion is a classical problem in data science wherein one attempts
to reconstruct a low-rank matrix while only observing some subset of the
entries. Previous authors have phrased this problem as a nuclear norm
minimization problem. Almost all previous work assumes no explicit structure of
the matrix and uses uniform sampling to decide the observed entries. We suggest
methods for selective sampling in the case where we have some knowledge about
the structure of the matrix and are allowed to design the observation set.
