  We propose orthogonal inductive matrix completion (OMIC), an interpretable
approach to matrix completion based on a sum of multiple orthonormal side
information terms, together with nuclear-norm regularization.
  The approach allows us to inject prior knowledge about the singular vectors
of the ground truth matrix.
  We optimize the approach by a provably converging algorithm, which optimizes
all components of the model simultaneously. We study the generalization
capabilities of our method in both the distribution-free setting and in the
case where the sampling distribution admits uniform marginals, yielding
learning guarantees that improve with the quality of the injected knowledge in
both cases. As particular cases of our framework, we present models which can
incorporate user and item biases or community information in a joint and
additive fashion.
  We analyse the performance of OMIC on several synthetic and real datasets.
  On synthetic datasets with a sliding scale of user bias relevance, we show
that OMIC better adapts to different regimes than other methods. On real-life
datasets containing user/items recommendations and relevant side information,
we find that OMIC surpasses the state-of-the-art, with the added benefit of
greater interpretability.
