  In matrix factorization, available graph side-information may not be well
suited for the matrix completion problem, having edges that disagree with the
latent-feature relations learnt from the incomplete data matrix. We show that
removing these $\textit{contested}$ edges improves prediction accuracy and
scalability. We identify the contested edges through a highly-efficient
graphical lasso approximation. The identification and removal of contested
edges adds no computational complexity to state-of-the-art graph-regularized
matrix factorization, remaining linear with respect to the number of non-zeros.
Computational load even decreases proportional to the number of edges removed.
Formulating a probabilistic generative model and using expectation maximization
to extend graph-regularised alternating least squares (GRALS) guarantees
convergence. Rich simulated experiments illustrate the desired properties of
the resulting algorithm. On real data experiments we demonstrate improved
prediction accuracy with fewer graph edges (empirical evidence that graph
side-information is often inaccurate). A 300 thousand dimensional graph with
three million edges (Yahoo music side-information) can be analyzed in under ten
minutes on a standard laptop computer demonstrating the efficiency of our graph
update.
