  The inductive matrix completion (IMC) problem is to recover a low rank matrix
from few observed entries while incorporating prior knowledge about its row and
column subspaces. In this work, we make three contributions to the IMC problem:
(i) we prove that under suitable conditions, the IMC optimization landscape has
no bad local minima; (ii) we derive a simple scheme with theoretical guarantees
to estimate the rank of the unknown matrix; and (iii) we propose GNIMC, a
simple Gauss-Newton based method to solve the IMC problem, analyze its runtime
and derive recovery guarantees for it. The guarantees for GNIMC are sharper in
several aspects than those available for other methods, including a quadratic
convergence rate, fewer required observed entries and stability to errors or
deviations from low-rank. Empirically, given entries observed uniformly at
random, GNIMC recovers the underlying matrix substantially faster than several
competing methods.
