  We consider the problem of performing matrix completion with side information
on row-by-row and column-by-column similarities. We build upon recent proposals
for matrix estimation with smoothness constraints with respect to row and
column graphs. We present a novel iterative procedure for directly minimizing
an information criterion in order to select an appropriate amount row and
column smoothing, namely perform model selection. We also discuss how to
exploit the special structure of the problem to scale up the estimation and
model selection procedure via the Hutchinson estimator. We present simulation
results and an application to predicting associations in imaging-genomics
studies.
