  We revisit the inductive matrix completion problem that aims to recover a
rank-$r$ matrix with ambient dimension $d$ given $n$ features as the side prior
information. The goal is to make use of the known $n$ features to reduce sample
and computational complexities. We present and analyze a new gradient-based
non-convex optimization algorithm that converges to the true underlying matrix
at a linear rate with sample complexity only linearly depending on $n$ and
logarithmically depending on $d$. To the best of our knowledge, all previous
algorithms either have a quadratic dependency on the number of features in
sample complexity or a sub-linear computational convergence rate. In addition,
we provide experiments on both synthetic and real world data to demonstrate the
effectiveness of our proposed algorithm.
